(CNN) -- American Airlines, already grappling with union issues and bankruptcy fallout, is now confronting a third problem: growing reports of loose seats.
On Tuesday, the company said another flight had experienced loose seats, bringing the total to three flights on two planes in a week.
A plane headed from Vail, Colorado, to Dallas on September 26 had seats come loose, the airline's vice president of safety confirmed Tuesday.
The same aircraft experienced a similar problem on a New York to Miami flight on Monday morning. That flight had to return to John F. Kennedy Airport.
Separately, a Boeing 757 from Boston to Miami carrying 175 passengers diverted to New York on Saturday when three seats in row 12 came loose shortly after takeoff.
The airline said it would inspect 47 Boeing 757 planes after the incidents.
"Originally, American planned to evaluate the seats on eight Boeing 757 airplanes, but out of an abundance of caution, the decision was made to proactively evaluate a total of 47 Boeing 757 airplanes that have the same model Main Cabin seats with a common locking mechanism," company spokeswoman Andrea Huguely said in a statement.
"American's internal investigation has focused on one of three types of Main Cabin seats on the 757s and how the rows of these three seats fit into the track that is used to secure the rows to the floor of the airplanes. Our maintenance and engineering teams have discovered that the root cause is a saddle clamp improperly installed on the foot of the row leg," she said.
The clamps were used on 47 of the company's 102 Boeing 757 airplanes.
So far, American Airlines has inspected at least 36 planes and found that six -- including the two involved in the recent diversions -- had seats that were not properly secured. Not all of the seats were loose, the company said, but they had the potential to become loose.
Eleven aircraft could be inspected Wednesday.
Huguely said the seats issue does not appear to be connected to any one work group or maintenance facility, and apologized for any inconvenience to customers.
"Safety is -- and always will be -- American's top concern," the spokeswoman said.
The Federal Aviation Administration is looking into the incidents of loose seats, which are the latest in a string of woes for American Airlines.
Earlier Tuesday, an American Airlines flight from Chicago to London made an unscheduled landing at Shannon Airport in Ireland after a passenger reported a smoky odor, an airline spokesman said.
American Airlines Flight 98, a Boeing 777-200 carrying 246 passengers and 14 crew members, was diverted as a precaution, airline spokesman Ian Bradley said.
An inspection revealed that the odor was coming from an overhead fan that had overheated, he said.
Niall Maloney, head of operations for Shannon Airport, said such technical diversions are not uncommon.
The airline has also been beset recently by labor troubles, delays and flight cancellations.
American, which filed for Chapter 11 bankruptcy protection late last year, persuaded a judge to throw out its contract with the pilots union last month.
Since then, the pilots have been engaging in what the airline calls a slowdown that has caused the number of flights that are delayed and canceled to skyrocket.
More than 1,000 American flights have been canceled and 12,000 delayed in the past month alone.
Airline management has blamed the situation on pilots filing what it claims are frivolous reports about aircraft problems. The pilots union has denied management's assertion.
Late Tuesday, a spokesman for the Allied Pilots Association said it would resume contract negotiations with the airline. Tom Hoban said talks could start as early as Wednesday. A company spokesman similarly said that negotiations are set to resume this week.
Meanwhile, Robert Gless, deputy director of the Air Transport Division of the Transport Workers Union of America, dismissed the notion that the problems with loose seats were linked to labor issues as "without any basis in fact."
Seat installation work is largely carried out by outside contractors, rather than maintenance personnel employed by the airline, he said in a statement.
"Problems related to seats are less likely a labor problem, but rather a management issue related to outsourcing work to third-party facilities," he said.
American Airlines plans to increase its use of outside maintenance facilities, including in China and other overseas locations, as it seeks to exit bankruptcy, he added.
CNN's Stephanie Halasz, Saskya Vandoorne, Sherri Maksin, Nick Valencia and Joe Sutton contributed to this report.