(FORTUNE Magazine) – Back in the days when Herb Kelleher was doing killer Elvis impersonations and wisecracking flight attendants had passengers rolling in the aisles, a scrappy Texas airline was built on a culture of fun. That worked so well that Southwest is now the nation's biggest carrier, in terms of passengers, and has the largest market cap. But where has the fun gone? After a grim tenure, Kelleher's successor, Jim Parker, recently quit as CEO. Now it's former CFO Gary Parker who must come up with some answers to a very unfunny question: Is success spoiling Southwest?

The problem with being the one profitable major airline, post-9/11, is that airline workers get avaricious. At the six bedraggled "legacy" carriers, unions have been making big wage concessions. At Southwest they've been making big demands. Its 7,200 flight attendants, whose starting pay was just $14,000, spent two bitter years seeking big raises and work-rule changes. They bridled against cleaning cabins between flights, for instance, which is one of those things that's given Southwest the industry's most productive workforce.

As long as Kelleher was around, employees would go the extra mile in the name of Herb. Prior to his retirement in 2001, "he was able to implement Southwest's unique cost structure and work rules," says an executive at another airline. "If you were a union leader, you couldn't badmouth Kelleher; he was an icon. But anybody new was going to be just another corporate executive."

The 73-year-old Kelleher was pressed back into service this spring in the stalemated, embittered flight-attendant negotiations. He got the deal done finally, but expensively: a 31% raise over the contract's six years. It's settlements like that--and a 2002 pilots' contract raising their pay a minimum of 20% over the past two years--that have sent Southwest's costs soaring. Its cost per average seat-mile of 8 cents is creeping closer to that of the legacy carriers--which is no way to continue being a successful discounter.

"It's worth asking whether Southwest is finally facing the same issues and challenges that legacy carriers have experienced for some time," wrote Morgan Stanley analyst William Greene on the day Parker quit and Southwest missed its second-quarter earnings number. "We believe there is a risk that as a generational change occurs and the oldest Southwest employees retire (who remember the early years of struggle), the company's low-cost culture will change."

To Michael Roach, airline consultant and former America West president, that has already happened. Southwest workers once saw themselves as industry outsiders and were motivated partly by feeling embattled. Now they mainly feel entitled. The result isn't exactly a midlife crisis, because Southwest is still the healthiest, richest U.S. airline. But it does represent the passing of a corporate culture and era. "The miracle at Southwest," says Roach, "is that it's gone on so long." --John Helyar