"We're working very diligently to gather all the facts related to our 757 seats issue," company spokesman Kent Powell said.
The Los Angeles Times reported Tuesday flights on Saturday and Monday suffered the same problem as a Vail, Colo., to Dallas-Fort Worth flight.
The parent company for American Airlines, AMR, filed for bankruptcy in 2011 and the airline has recently announced 11,000 layoffs. But American said disputes with labor, including stalled contract talks with the pilots' union, are not behind the problem with seats coming lose in flight.
"Our maintenance teams continue to inspect aircraft in our 757 fleet to determine what caused the issue," Powell said.
"We are certainly curious about what is going on," said Gregg Overman, a spokesman for the Allied Pilots Association.
Last week, an AA executive accused the company's pilots of effecting a work slowdown. Among the tactics for slowing down productivity, pilots were using maintenance check orders to create delays, the executive said.
Pilots union leaders were expected to announce Tuesday whether they would return to the negotiating table with the airline.
Celebrity Families of 2014 [PHOTOS]