The airline said it has completed inspections on 36 of those planes and plans to check the remaining 11 soon. The Federal Aviation Administration is also looking into the problem.
The seat snafus come as American Airlines, whose parent company, AMR, filed for bankruptcy last year, struggles to cut costs and wrap up contract negotiations with its 10,000 pilots.
All along, American Airlines officials insisted that the loose seats had nothing to do with its labor problems. But over the past two weeks, hundreds of flights had been delayed and canceled, and the carrier has blamed its pilots for submitting maintenance work orders shortly before takeoff.
The union has insisted that it did not order its members to cause such delays and cancellations.
(In the video above, Times consumer columnist David Lazarus and travel industry reporter Hugo Martin discuss the latest developments in the story.)
Follow Hugo Martin on Twitter at @hugomartin