MONTREAL >> A trade group representing hundreds of airlines is renewing its push for additional pilot training and coordination among global aviation regulators to ensure that the Boeing 737 Max is safe before it is allowed to fly again after two deadly crashes.

If additional training is required, including the possible use of scarce MAX flight simulators, it could come at a tremendous cost to Boeing and further delay the plane’s return.

Airlines are already adjusting their schedules with the expectation that the plane will remain grounded for an extended period.

Southwest Airlines said Thursday that it has taken the Max out of its schedule for another month, through Oct. 1. Southwest is the fourth-biggest U.S. carrier by revenue and has more Max jets — 34, with about 250 more on order — than any airline in the world.

Southwest’s announcement was the latest case of a major airline dialing back its hopes for a speedy return of the Max. United Airlines did the same thing Wednesday. The plane was grounded worldwide in mid-March, but airlines hoped that Boeing would fix problematic flight-control software quickly enough so that the planes could be back in service in June.

The Max’s return took another detour this week after U.S. government test pilots working in a flight simulator discovered another flaw in the plane’s computer systems that could push the nose down. That condition, called runaway stabilizer trim, occurred in the Max accidents in Ethiopia and Indonesia that killed 346 people where pilots were unable to control the planes, according to preliminary reports by investigators.

The Federal Aviation Administration is requiring Boeing to fix the new flaw, a step that is expected to add from one to three months to the plane’s return.

The Washington Post reported today that before the Max began flying, the FAA repeatedly found safety lapses at Boeing and ordered the company to fix them, but Boeing failed to do so. In 2015, Boeing agreed to pay a $12 million settlement and make changes to ensure that it was complying with safety regulations.

Boeing has been under intense scrutiny since October, when a Lion Air Max plunged into the Java Sea off Indonesia shortly after takeoff. Boeing began updating the flight-control software implicated in the crash — it pushed the plane’s nose down more than two dozen times based on faulty readings from a single sensor.

The update was not complete, however, by the time an Ethiopian Airlines Max crashed in March. Again, the nose-down pitch occurred. Pilots initially followed Boeing’s prescribed response, but it didn’t work, possibly because the plane was flying too fast.

Pilot training has emerged as a central part of fixing the plane. Boeing wants computer-based training, and FAA technical experts agree that would be sufficient.

Others, however, believe pilots need to practice with the new Boeing software in flight simulators. Earlier this month, Chesley “Sully” Sullenberger, who landed a crippled airliner safely on the Hudson River in 2009, told a House subcommittee that pilots should get simulator training.

That, however, would pose a problem for Boeing and the airlines — it could take weeks or months to find simulator time for every pilot who flies the Max. Southwest and American Airlines each have thousands of Boeing 737 pilots, but neither airline has a Max simulator. Boeing has one in Miami and a similar machine in Seattle.

At a meeting in Montreal of regulators and airline representatives, the head of the International Air Transport Association, Alexandre de Juniac, made an appeal for coordination between aircraft operators and regulators.

De Juniac and his airline group are trying to repair the fragmented regulatory approach to the Max. In March, other countries grounded the plane despite the FAA’s initial view that it was safe even after a second crash.

Regulators in Europe, China and Canada have indicated they want to conduct their own reviews of the FAA’s 2017 certification of the plane, which could further complicate and delay the Max’s return to flying.

Shares of Boeing were down $7.35, or 2%, to $367.59 in afternoon trading.