We both just end up getting too tired. I can climax multiple times, but I don't understand why he can't. Is there something I can do? Should he see a doctor? He thinks it's psychological, but he doesn't know what exactly the reason is.

Since he can achieve orgasm, it’s not physical, but psychological. I can’t tell you exactly what is going on and he should consult with a sex therapist. The therapist should be able to help him overcome this problem, which is called retarded ejaculation. It’s much more common during intercourse, when there are potential distractions, than during masturbation, but a sex therapist should be able to offer him the assistance he needs to overcome this condition.