Problems at the beginning of the month are actually pretty common because sometimes the two monthly schedules aren't compatible with crew scheduling policies.

For example there is a rule that says they can't fly for seven consecutive days without at least a 24 hour break. A pilot may have a 4 day trip ending on the last day of the month and then his new schedule has another four day trip starting the first of the new month. This would violate the seven day rule so AA would remove him from the entire trip (all four days). He is obligated to try to make up the time but not on the same days, just some time during the month.

Other problems that could have caused the same result would be minimum rest time violations (arrives late the last night of the month and leaves really early the first day) and 30 in 7 (fly 30 hours in seven days)

AA pilots love to game the system and they will intentionally try and bid themselves into these situations so they can get extra days off.