Remember there are a couple of different types of bankruptcy (reorginization and liquidation) and that the US government will step in when a too important business is about to fail. Some smaller airlines might disappear from time to time, but the big ones will continue to operate even if they go through a bankruptcy or three. The gov will step in with tax payers dollars to keep them going if they can't come to terms with the banks they owe money to.

Of course, they will be forced cut costs as much as possible and that means axing the less profitable and nonessential flights. I have no idea of how profitable the Belize flights are or whether anybody feels they are a neccessity.

I guess what I am trying to say is don't panic. Odds are good in the case of a large airline going bankrupt that your flight will still happen and if it doesn't you will likely get a refund. If you are still concerned, call the airlines.