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:

Labor Negotiations

In 2003, AMR’s unions saved the carrier from bankruptcy by making deep salary cuts of up to 35%. Eight years later, they’re looking to get some of that money back. The good news for AMR: The all-important pilots’ union has resumed contract negotiations. The bad news: An APA spokesman admitted Tuesday that pilots are worried about American’s viability and the impact of bankruptcy on pensions. That could make negotiations tougher for the carrier and further concessions less likely.

Slowdown in Air Cargo and Travel

The tough economy is hammering global air-freight demand. The international airline group IATA says the global air freight market dropped 3.8% in August and air cargo volume has fallen by half this year. While passenger traffic is stronger, growth is declining: July growth was 5%; August growth fell to 4.5%.

Expensive Borrowing

AMR borrowed $725.7 million last week, secured by 43 aircraft. The money will go to pay a portion of some $1.3 billion in debt that comes due in the second half of this year. While credit still is available, the airline had to pay a premium to get it: reportedly as high as 8.75%. That reinforces fears about AMR’s continued viability.

Challenging Fundamentals

American is the only major airline to lose money this year — and analysts believe it will keep on losing money through 2012. At $2.39, the stock is trading more than 73% below its 52-week high of $8.98 last November. With a market cap of only $801.14 million, the stock has a price/earnings-to-growth ratio of -0.3, reflecting the fact that the airline is losing money. It also has levered free cash flow of -$1.48 billion.

As of this writing, Susan J. Aluise did not hold a position in any of the stocks named here.