What if they did go belly up, would that keep anyone from enjoying this hobby? Not I.
Wanna bet. Who do you think would be directly involved in enforcing RC flying if the AMA couldn't handle the job? Simple, the FAA since it's their airspace. This means the FAA could easily mandate restrictions directly to the states with one swift blow.
As far as AMA's break even point, I think they are there right now or getting real close. Either way it doesn't matter, they need members.