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"While it is likely that injunctive relief would ease American's operational problems in the short term, it is equally likely that this measure would permanently eliminate this management team's ability to obtain a consensual agreement with APA," Goldberg warned in a research note Thursday.

Customers have used social media to vent their frustration and to tell American and its pilots what they think about the dispute.

"If you're a business traveler and you need to be at a meeting at 10 a.m., are you going to fly that morning and risk it?" Seaney said.

"When it comes to me not making a meeting, that's your bread and butter for business travelers, and that's where the airline starts to get hit in the revenue."

American is fortunate that the labor dispute began in September during a slower travel period as opposed to the busy holiday travel season, industry analysts said. But if the slowdown continues another two weeks, leisure travelers purchasing Thanksgiving and Christmas tickets are likely to choose a carrier other than American.

"People do book away, and what you have to do to get them back is you have to lower your fares enormously," said airline consultant Darryl Jenkins. "It's time for both sides to work something out because travelers are being hurt by this."

Eastern Airlines was in financial trouble for much of the 1980s. When the machinists union decided to strike in 1989, pilots and flight attendants also chose to not cross the picket line.

Then-Chief Executive Frank Lorenzo hired replacements to run the airline while it was in bankruptcy but continued to lose money until, in 1991, the airline finally shut down and liquidated.

While industry analysts say American's pilot dispute hasn't reached Eastern's level of animosity, a significant amount of distrust exists between management and the union.

"The dispute here seems to now be going beyond economic considerations to the emotional level, which is always dangerous since rationality for all parties can become secondary as was in the case of Eastern," Maxim Group analyst Ray Neidl wrote in a note to investors Wednesday.

While the American situation is nowhere near Eastern's labor-management toxicity, Neidl said, "we do remain concerned that it could escalate in what is a weak economy and if not resolved could lead to a possible further weakening and eventual liquidation of the company."

Unlike at Eastern, analysts think American's unsecured creditors committee may become more involved if the labor situation deteriorates even further.

"The creditors will not allow an Eastern situation because that was a piece-meal liquidation where there were not high recovery values realized by the creditors and it was a very, very bad thing for employees," said Ken Malek, of Conway MacKenzie, a financial turnaround and crisis management firm. "The airline is going to start suffering revenue-wise, which will make it even more difficult to come to terms with the employees."

American's parent company, AMR Corp., is required to file monthly financial reports with the bankruptcy court. Last week, it posted an $82 million loss for August. September results, which could include the impact of cancellations and flight delays, will be reported in late October.

Referring to the liquidation of Eastern, Wilson said in an interview Friday: "We are married to the corporation, so we certainly don't want to go that route."

That said, the union leader added: "The lack of trust that we have for the corporation's management decisions and their ability to understand the concerns of the general employee population, and most definitely the pilot population, makes it very tough for us to work with them."