Lesley Popovits ^[1] sued her former employer Circuit City Stores, Inc. and Travelers Managed Care System, ^[2] alleging that they improperly failed to provide her continuing health insurance under the Consolidated Omnibus Budget Reconciliation Act (COBRA), 29 U.S.C. §§ 1161-1168, after Circuit City terminated her employment. COBRA requires employers to continue providing benefits coverage for up to eighteen months after releasing an employee from employment. See 29 U.S.C. § 1162. Popovits contends that following her election of COBRA benefits, Circuit City sent a letter to her improperly demanding a premium payment covering a period for which she did not need continuing coverage. The district court concluded no genuine issues of material fact existed between the parties and granted Circuit City’s motion for summary judgment. We reverse and remand the case for further proceedings.

Between October 1993 and July 1994, Circuit City employed Popovits in its Evergreen Park, Illinois, store and provided her with employee benefits, including medical coverage. It discharged her for gross misconduct. Under these circumstances, Circuit City chose not to extend health benefits coverage to her under COBRA. Popovits appealed this decision and was awarded COBRA benefits in October 1995. Deciding not to challenge this decision, Circuit City notified Popovits by mail in December 1995 that she could elect COBRA coverage. Until that point, Popovits had been without medical coverage for seventeen months. Two months later, she elected coverage by executing the necessary form and returning it to Circuit City. After receiving her acceptance of the COBRA coverage, Circuit City mailed her another letter explaining the retroactive nature of the benefits and the manner by which she had to tender payment.

[*729] Because Popovits obtained medical coverage after February 1995, she sought only coverage for seven months — the period between the termination of her employment and the beginning of her new coverage. She did not pay Circuit City any amount before the required date specified in the letter requesting payment for the reinstatement of the retroactive benefits. She claims that she did not pay the amount because she was trying to contact Circuit City to discuss the total amount of the initial payment, but that it refused to discuss this problem with her or her attorney. Circuit City denies Popovits or her attorney made any such efforts. As a result of her failure to tender payment, Popovits lost her statutory right to obtain any retroactive coverage.

Popovits, then, filed suit against Circuit City. In her complaint, she charged that Circuit City had violated COBRA by demanding an improper premium payment. After the parties conducted discovery, the district court ordered the parties to file simultaneous motions-for summary judgment. The district court also required the parties to file simultaneous responses to these motions. It did not permit either side an opportunity to file a reply. The district court found no issue of material fact existed, granted Circuit City’s motion for summary judgment, and denied Popo-vits’s motion. Popovits, then, moved to amend this judgment, asking for relief from operation of the judgment and the opportunity to respond to the Circuit City’s denial in its response that Popovits had attempted to contact Circuit City about the initial payment amount. As part of the motion, Popovits provided the district court with an affidavit from her attorney noting his efforts to discuss payment for COBRA coverage with Circuit City. This affidavit counters the affidavit of Circuit City employee Nancy Brooking, which Circuit City submitted for the first time in response to Popovits’s motion for summary judgment. Because of the manner in which the district court scheduled the filings for summary judgment, Popovits did not have an opportunity to respond to Brooking’s affidavit before the court ruled on the motions for summary judgment. Popovits’s attorney stated in his affidavit that he called Brooking, who said that Popovits’s “claim would not be considered until [she] made her full premium payment” even though he explained Popovits needed coverage for a shorter period than indicated by the premium payment. After this conversation, Popovits’s attorney avers in his affidavit, Circuit City sent the February 9, 1996, letter demanding payment in full and refused to take or return the attorney’s phone calls.

The district court denied Popovits’s motion to amend the judgment. Pursuant to her appeal, we consider whether the district court properly refused to grant Popo-vits’s motion to amend the judgment and correctly granted summary judgment in favor of Circuit City after concluding no genuine issue of material fact existed between the parties.

We first address the district court’s refusal to consider the affidavit submitted by Popovits’s attorney with her motion to amend judgment. Popovits filed a motion to amend judgment pursuant to Rule 59 of the Federal Rules of Civil Procedure and, alternatively, Rule 60 of the Federal Rules of Civil Procedure. We characterize substantive motions to alter or amend, such as this one, as motions under Rule 59(e) if they are served within ten days of the entry of judgment. See Britton v. Swift Transp. County, 127 F.3d 616, 618 (7th Cir.1997); Billups v. Methodist Hosp., 922 F.2d 1300, 1305 (7th Cir.1991). We compute the ten day period by excluding the day of the event (in this case the entry of judgment). We also exclude Saturdays and Sundays from the count because the period of time prescribed is less than eleven days. See Fed.R.Civ.P. 6(a); see also Kunik v. Racine Co., 106 F.3d 168, 172-73 (7th Cir.1997). The district court entered judgment on June 3, 1998. Popovits filed her motion to amend the judgment on[*730] June 15, 1998. Although the actual time span is twelve days, once weekend days are excluded pursuant to the federal rules, Popovits’s motion comes within the ten day allowance. Thus, we will treat her motion as one brought pursuant to Rule 59(e).

We review a district court’s decision on a Rule 59(e) motion under an abuse of discretion standard. See In re Prince, 85 F.3d 314, 324 (7th Cir.1996). While this review is deferential, it is not merely a rubber stamp. Cf. Money Store, Inc. v. Harriscorp Finance, Inc., 885 F.2d 369, 372 (7th Cir.1989) (explaining the abuse of discretion standard in the context of Federal Rule of Civil Procedure 60).

In her Rule 59(e) motion, Popovits asserts that a material issue of fact exists as to whether she and her attorney attempted to contact Circuit City to resolve the dispute about the amount Circuit City expected her to tender for the coverage. She supports this statement with an affidavit from her attorney in which he states that he tried to contact Circuit City, but that its employees refused to discuss the problem with him. This assertion, which had been made in the original 12(M) statement, counters the affidavit of Brooking, Circuit City’s Senior Benefits Analyst at the time, that Circuit City filed with its response in opposition to Popovits’s motion for summary judgment. Brooking’s affidavit states that neither Popovits nor her attorney contacted Circuit City to resolve the issue.

While Rule 59(e) permits parties to bring to the court’s attention errors so they can be corrected without the costs associated with appellate procedure, “[t]he rule does not provide a vehicle for a party to undo its own procedural failures, and it certainly does not allow a party to introduce new evidence or advance arguments that could or should have been presented to the district court prior to the judgment.” Moro v. Shell Oil Co., 91 F.3d 872, 876 (7th Cir.1996). However, if an issue arises to which a party does not have the opportunity to respond, granting the motion to amend may be appropriate. See In re Prince, 85 F.3d at 324.

Popovits has a valid argument that the district court abused its discretion when it refused to consider the affidavit of Popo-vits’s attorney and denied her motion to amend. In her complaint, Popovits charged that Circuit City did not respond to her requests for claim procedure. She included this allegation in her 12(M) statement of uncontested fact and motion for summary judgment. ^[3] The district court denied Popovits the opportunity to extend the discovery period to depose Circuit City employees to aid her in establishing material issues of fact before requiring the parties to file summary judgment. After Popovits filed for summary judgment, Circuit City contested her assertion in its 12(N) statement and submitted Brooking’s affidavit as support for its denial. It filed these documents with its response in opposition to Popovits’s motion for summary judgment. Pursuant to the district court’s order, the parties filed simultaneous cross motions for summary judgment and cross responses. The district court did not permit either party to respond to issues that arose in the cross responses. We find this situation troubling, see Retired Chicago Police Ass’n v. City of Chicago, 76 F.3d 856, 867 (7th Cir.1996) (finding a similar expedited procedure problematic), because Popovits was not afforded an opportunity to respond to this new challenge to her claim. Thus, the district court erred and[*731] should have considered her attorney’s affidavit.

We next turn to consider whether in light of this affidavit the grant of summary judgment was appropriate. It was not. We review the district court’s decision de novo. See Tesch v. County of Green Lake, 157 F.3d 465, 471 (7th Cir.1998). Summary judgment is proper when “the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” Fed.R.Civ.P. 56(c); see also Celotex Corp. v. Catrett, 477 U.S. 317, 322-23, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). In determining whether a genuine issue of material fact exists, we construe all facts in the light most favorable to the nonmoving party and draw all reasonable and justifiable inferences in that party’s favor. See Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). However, neither “the mere existence of some alleged factual dispute between the parties,” Anderson, 477 U.S. at 247, 106 S.Ct. 2505, nor the existence of “some metaphysical doubt as to the material facts,” Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 586, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986), is sufficient to defeat such a motion.

COBRA requires that employers offer qualified beneficiaries continuation coverage that “is identical to the coverage provided under the plan to similarly situated beneficiaries under the plan with respect to whom a qualifying event has not occurred” for a maximum period of eighteen months. 29 U.S.C. § 1162(1), (2)(A)(i). Among those who are considered qualified beneficiaries are those employees terminated for reasons other than gross misconduct. See 29 U.S.C. § 1163(2). The qualified beneficiary must pay the applicable premium in a timely manner or risk losing coverage. See 29 U.S.C. § 1162(2)(C). The applicable premium is “the cost to the plan for such period of coverage for similarly situated beneficiaries with respect to whom a qualifying event has not occurred.” 29 U.S.C. § 1164(1). Thus, if Circuit City demanded that Popovits, who the parties agree is a qualified beneficiary, pay a premium that does not correspond to the statutory requirements because it requires her to pay a premium greater than that required for other employees seeking the same period of coverage (seven months), it has violated COBRA.

Popovits’s claim is that Circuit City did just that. Her argument boils down to the belief that Circuit City demanded an improper premium payment from her by not adjusting the amount requested to account for only those months she wished to receive coverage — less than eighteen — and by refusing to discuss any adjustments with her. Circuit City denies engaging in any such conduct, pointing to Brooking’s affidavit, and claims that the February letter it sent to Popovits clearly spelled out her right to tender less than the full amount demanded. Although the district court agreed with Circuit City, we do not.

The February letter provides that upon receipt of the initial payment (which is the amount Circuit City required to be paid before it would reinstate coverage), Popo-vits would receive retroactive coverage from August 1, 1994, until the earlier of the maximum period of continuation (the eighteen months required under COBRA), her obtaining coverage under another health plan, her obtaining Medicare coverage, her failure to make the required payments, or Circuit City no longer providing group health care to any of its employees. It also stated:

THERE IS NO EXTENSION OF THE INITIAL PAYMENT DUE DATE. You may pay the Initial Payment in installments; however, the full amount must be paid by the Initial Payment due date. If the full Initial Payment is not made by the due date, coverage will be continued through the date payment was made.

[*732] (emphasis in original). Circuit City calculated the initial payment as $2572.02, based on the cost for providing coverage to Popovits for the entire eighteen month continuation coverage period. Although Circuit City argues that the letter clearly stated she need not elect the entire eighteen month period of potential coverage, nothing in the letter indicated that she could tender less than the entire amount of the initial payment. It also provided:

The Initial Payment of $2572.02 must be received by the Circuit City Stores COBRA Administrator on March 23, 1996. THERE IS NO EXTENSION OF THIS INITIAL PAYMENT DUE DATE.... Subsequent regular monthly payments must be received by the last day of the month after due date or cancellation will result.

(emphasis in original). In addition, the letter provided a phone number and stated, “Please contact COBRA Administrator ... if you have questions about continued coverage.”

The dueling affidavits from Popovits’s attorney and Brooking, in which she denied Popovits or her attorney attempted to contact Circuit City to discuss the payments, create a genuine issue of material fact as to whether Circuit City refused to discuss the amount of the premium. Clearly, the parties dispute whether any attempts to discuss the February 1996 letter were made or rebuffed. Circuit City suggests that this factual dispute is irrelevant because, as the district court noted, the plain meaning of the letter, which has nothing to do with contacts between Popovits and Circuit City, controls the outcome of the case. It asserts that providing the letter constituted sufficient notice under COBRA and that it had no responsibility to answer questions about the plan, even though it assured its employees that it would. We disagree. If, as Popovits and her attorney assert, Circuit City refused to discuss the amount of the premium payment before Popovits paid the entire initial payment, regardless of the clarity of the letter, it is arguable that Circuit City demanded an improper premium payment in violation of COBRA. Demanding a payment for an amount of time in excess of that requested by the beneficiary would constitute an improper premium payment under the statute. See 29 U.S.C. § 1164(1). Thus, the resolution of the dispute about the contact between these parties goes to the heart of Popovits’s claim.

As a result of this analysis, we believe the grant of summary judgment in favor of Circuit City was inappropriate because of the existence of a material issue of fact. In addition, under the standard for summary judgment, a court should construe all facts and reasonable inferences in the light most favorable to the nonmoving party, in this case Popovits. In granting summary judgment, the district court appears to have inappropriately read the inferences in favor of Circuit City rather than Popovits.

Therefore, we find that the district court abused its discretion by refusing to consider the affidavit of Popovits’s attorney and erroneously permitted the grant of summary judgment in favor of Circuit City to stand. Thus, we Reverse the grant of summary judgment in favor of Circuit City and RemaNd the case for further proceedings consistent with this opinion.