The only time I ever black out is during the Elite Four, because if you're not leveled enough, fighting the 5 strongest trainers in the land one after another can actually be quite difficult :P In fact, depending on the games (HG/SS, for example), I'll sometimes go into the Elite Four with the full expectation that I'll black out a few times before I'm strong enough to actually beat them. This isn't a big problem in HG/SS, because I can just leave all my money with my mom, so I don't lose any.
Now the question I've always wondered is, why the heck does the player black out when they're beaten in a battle? o: