Odds of Hanging On
It depends. You actually have a better chance of sticking around if you're a musician who's aligned herself with a regular company or orchestra than if you're a superstar singer who has suddenly burst onto the scene. Superstars tend to fizzle out and vanish with freakish regularity, so even if you're that one in a million who makes it, you may also be one of those 99 of 100 who don't hold onto it for long.
If you're one of the majority, however, and are just trying to get enough regular gigs to keep the money coming in, you'll need to work hard to become established, known, and respected within the industry, and then you should have a pretty decent shot of getting by. Ah—"getting by." The American Dream.