By Chris Isidore, CNN Business

American Airlines has a big problem with canceled flights. The 737 Max grounding isn't helping, but it is not the primary cause of its troubles.

In June, American Airlines canceled about 4% of its scheduled flights, according to data tracker masFlight. American's canceled flight rate is twice the rate of Southwest, and is more than six times that of United Airlines, according to masFlight. It is nearly 20 times the cancellation rate at Delta.

That 4% doesn't count the 115 cancellations American has made every day because of the 737 Max grounding. Those flights weren't counted because they were already taken off the schedule weeks before the date they were originally scheduled.

American Airlines has two dozen 737 Max planes in its fleet. The 737 Max cancellations represent about 1.5% of American's schedule. It said Wednesday the 737 Max cancellations had cost the airline about $185 million in the just completed quarter.

So if it's not just the 737 Max, what's behind American's cancellation crisis?

American alleges that a major part of its flight cancellations are because of an ongoing labor dispute with the two unions representing its mechanics. The airline says mechanics are deliberately grounding planes as a way to put pressure on the airline during negotiations over a new contract. It has filed federal lawsuits against the unions.

The unions deny the airline's allegation.

"Our members value American Airlines fliers and work hard every day to ensure they have the best experience possible," said the Transport Workers union, one of the two unions representing mechanics. It said that American should return to the bargaining table rather than fighting the unions in court.

Despite American winning some preliminary decisions in the case, it argues in court filings that the mechanics continue to improperly ground planes. It says aircraft that were out of service due to maintenance issues is averaged more than 50 a day, up about 30% from the average during previous summers. It reached a high of 66 grounded planes because of maintenance issues on June 18, which the airline said is one of the highest totals in the airline's history.

"The continuing disruption is causing devastating harm to American and its customers, employees and brand," said the airline in a court filing.

The problem from the labor dispute is far more serious than the one involving the 737 Max, said airline consultant Michael Boyd.

"Not carrying people on a flight that was never booked isn't that big a deal. Leaving people at the gate because the airplane is broke and there's no plane to replace it is a much bigger issue," he said.

And in the age of social media, people who run into problems traveling on American are more likely to spread the word, discouraging others from booking on the airline in the future he said.

"The problem with American is people talking about this and deciding to look elsewhere for their flights," said Boyd.

The good news for American is that the planes that are flying are full, and the fares are higher than it originally projected. Fuel prices are also lower than its original estimate for the second quarter.

The guidance it gave on fares and operating costs helped lift shares of American and other airlines in Wednesday trading, despite the news about the flight cancellation problems.