Staying alive isn't always very meaningful. In the biggest tournament I ever played, which was live with a multi-million prize pool, I outlasted nearly half the field. The main reason was that I was card dead.
The main thrust of advice I've seen for when you're playing opponents above your ability level is to be more aggressive than usual with your good hands. Since you can't count on out-playing them, the idea is to try to make the most of the times when you get cards. I haven't read them, but I gather that's the gist of the the Kill Phil book, which is about playing stronger opponents.
How'd you end up?