after an hour or so, I won't be able to make it up the course I went up the first time.

Yeah, to begin with, 45 minutes (including breaks) was about my maximum length session before I was useless. Now (for indoor bouldering) it's about two and a half hours.

So you'll develop more endurance as you go along.

Though it's also helpful to work on pacing yourself (something I should admit I'm very bad at). With bouldering in particular, it's easy to keep on trying and trying and trying on a problem and getting worse each time, when taking five minutes off can let your body recover.