The odds of them shutting down in the next year or so are very slim. Not to imply that they are likely to shut down at all, but they are likely nowhere near that point.
Even if Frontier were to be cut loose from their parent company Republic (a profitable company) and file chapter 11 on their own, usually it takes a long time for an airline to die in the modern age. Midway filed for Chapter 11 in August of 2001 and flew for two more years before finally shutting down. Vanguard was a similar situation. Even Independence, which was a tunnel with no light at the end and burned through money at a stunning rate, lasted a couple of months after chapter 11 before shtudown.
Back a few decades to upstart examples like Pride Air, Air South, and McClain, those
were comparably tiny, fledgling airlines, often with relatively thin capitalization and not much of a safety net. Frontier is in a different situation than those airlines were back then.
Again, I don't see any reason to think that Frontier is destined for shutdown. But if things do deteriorate, the cold question of "will they shut down and strand me?" is still very likely no.
If you'd like, link over to this thread from several weeks back for more discussion of a similar question:
http://www.flyertalk.com/forum/front...e-trouble.html