Shares of American Airlines parent AMR Corp. (NYSE:AMR) reversed course Tuesday, surging more than 20% over Monday’s close of $1.98. The stock had been hammered Monday, sinking some 33% on a volume of nearly 77 million shares — average daily volume is about 12.8 million.

The selloff was triggered by new fears that American might be forced to declare bankruptcy. Investors took news of pilot retirements that were 10 times higher than normal during the past two months as a sign that pilots were afraid of the adverse impact a Chapter 11 filing would have on their pensions.

The Allied Pilots Association, which represents American’s 10,000 pilots, attributed the retirements as fruit of a volatile stock market and a change in pilots’ mandatory retirement age — not bankruptcy fears. That helped the stock rebound Tuesday.

While airline executives are on record that bankruptcy is neither the goal nor the preference, there is growing concern that AMR has only two real options for survival: bankruptcy or acquisition by another carrier.

Carriers like United Continental (NYSE:UAL), Delta Air Lines (NYSE:DAL) and US Airways (NYSE:LCC) filed for bankruptcy during the past decade and emerged stronger — they were able to slim down operations and offload many aged, gas-guzzling planes. Mergers have delivered value, too. US Airways, which missed out on many of the big merger deals, could be an attractive partner for American.

Despite its challenges, AMR cannot be counted out as circling the drain; there’s still plenty of value left in the franchise. And the stock is trading at very cheap prices, even after Tuesday’s recovery. That being said, here are four reasons to doubt the bounce in AMR shares: