They are normally open on weekends albeit with reduced hours:
AAdvantage Customer Service
1-800-882-8880
(or your Elite Service Desk telephone number) Please say "AAdvantage Account" when prompted at the Main Menu.
7:30 a.m. - 9:00 p.m. (CT) Monday - Friday
7:30 a.m. - 7:00 p.m. (CT) Saturday
10:30 a.m. - 7:00 p.m. (CT) Sunday

I'm not sure what makes this weekend extra special to the point that they wouldn't a least field skeleton crew. But it is not a time is of the essence situation so here's hoping they come back rested and raring to provide CS on Tuesday.