If you want "long-term" stability, it has to be Southwest (WN). They've been in the game for thirty years and seem to have determined the right strategy to survive both now and into the future.

But it depends on what you want. WN's FF program will not get you anywhere WN does not fly - period. So no international, much less a good chunk of the domestic US.

But if all your travel is confined to city pairs that WN serves, and you don't mind their in-the-air product, it's pretty hard not to pick them. Every fifth flight free and consistently low fares.

If you want more bredth of destinations and service, my money (for the short term) is UA or AA. Yes, UA is in C11 and AA was almost there, but both airlines have not recently made significant reductions in their FF programs in an effort to encourage high-fare frequent flyers and discourage low-fare frequent flyers. It remains to be seen how much revenue those low-fare frequent flyers who decide to abandon DL/CO/NW (if and when they follow) will take to UA and AA and what kind of effect it will have on the bottom-lines of the airlines losing them and gaining them.