If you've booked upcoming travel on AA to SJO or elsewhere, have a look at the advice printed in large, friendly letters on the cover of your Hitchhiker's Guide: DON'T PANIC.
You might want to read
this web page about airline bankruptcies in general. Looks to be pretty recent info, as it refers to bankruptcies that were news about a year ago.
Most airlines continue operating while in BK. That is, after all, the point--for the airline to continue operating while they shed debts and obligations. However if it really bothers you, you might want to consider buying trip insurance before the airline actually enters BK, because it'll be impossible afterwards.
One effect of the bankruptcy may be some readjusted schedules or canceled flights. Odds are they'll still get you where you want to go on the day you want to go there, but there is an increased risk of being bumped, and your flight time may get moved to a time that's anywhere from "inconvenient" to "doesn't fit my schedule at all." It's up to you to work out with the airline what to do in that case, but you may be SOL if you can't get on the rescheduled flight they give you. (Not really sure what your rights might be in a situation like that.)
All that said, I'm glad I'm booked on DL.
