The Allied Pilots Association Union is blaming a glitch in the system for the error, while the airline insists they aim to run all scheduled flights over Christmas.
American says the staffing snafu caused by a glitch in its pilot scheduling system is almost resolved.
And while the number of affected flights represent a relatively small percentage of the more than 90,000 flights that American will operate during the two-week period, flights are expected to be packed, thus leaving less wiggle room for re-accommodating affected fliers.
It is now being reported that the airline is offering pilots time-and-a-half to cover flights over the busy few weeks during the holidays.
The APA said it has responded by filing a Presidential Grievance, and said that neither it nor the contract between APA pilots and the airline can guarantee the promised payment of the premium being offered.
The scheduling problem has left flights from some of American Airlines' biggest hubs without pilots including Miami, Dallas-Fort Worth, Chicago's O'Hare and New York's LaGuardia Airport, without pilots, according to a memo from the airline to pilots, which was seen by CNBC. The computer said, 'Hey ya'll. Reserve pilots, however, can only pick up flights 24 hours before departure, so the flights that they are eventually assigned to are now unclaimed. You want the days off?
The airline did not say how many flights were affected or the exact time period of affected flights.
The airline said: "We're working diligently to address the issue and expect to avoid cancellations this holiday season". The airline has declined to quantify the potential number of flights involved.
"That number of open flights continues to decrease thanks to our pilots who are stepping up to the plate and picking up trips to ensure customers are taken care of", Aran Coello said in a statement.
"I'm watching a "Grinch that stole Christmas" thing happening", he added to Reuters.
The APA statement reads: 'On Friday, management disclosed a failure within the pilot schedule bidding system.
"We are being told to expect business as usual", said Beardsley.