I disagree with Evo. I wouldn't say he's not cut out for it just because he sometimes experiences difficulty and stress.
"Big" results in theoretical physics are hard to come by, at least in the high-energy field. In this field, theory has stretched so far beyond the reach of experiments that there is no way to judge what is an important result and what isn't; whether a paper turns out to be important has more to do with whether it gains popularity (which in turn has to do with a lot of other factors including whether it is understandable or easily applied to other problems).
I believe condensed matter theory is somewhat difficult as well. However, quantum information theory seems to have a lot going on, and theoretical biophysics is wide open, unclaimed territory.
Anyway, I work in high-energy theory, and I sometimes experience the things you describe (minus the anger and the feeling like it's a waste of time). Problems are open-ended, and a good approach to solving them is not always clear. You have to try things to get an idea of what works, and you will frequently backtrack due either to trying the wrong thing, or making a mistake. Sometimes I have to completely redo someone else's work because there is a typo in their paper, etc.
For the things that I work on, you have to enjoy playing around with the math, which is something I spend many hours doing. It is occasionally frustrating when I can't figure out how to proceed, but when I eventually do, the "A ha!" feeling outweighs the earlier frustration. One thing that motivates me through the frustrating part is that I'm the one who dared go down the path, however difficult it is, and I'll be the one to find and share the result (it helps to know that the result is expected to have some value or beauty, of course).
I don't feel that my results are "small" or unimportant (I have found whole infinite families of classical solutions to various supergravity theories), but they are not huge either. Any given result in high-energy theory today has a small audience; there will not be another Einstein or Feynman for a very long time, because today high-energy theoretical physics is very disconnected from experiment.
I can tell you my biggest sources of stress are these:
1. Looming graduation and the uncertain future beyond that. Will I get a job in physics that pays enough? If not, what will I do?
2. Spending so much time working on problems that I neglect other things, like going to the beach or cleaning the office.
The reason for spending so much time working is partly because I enjoy it, partly because I get an idea and I'm excited to try it and see where it leads (which may take many hours of doing math), and partly because I'm feeling some pressure to finish some more papers quickly, due to #1.
But even though the math is fun to play with, it can get depressing to allow the apartment to fall into disarray, or to miss out on social activity. Striking a balance is important.
I say, if he is merely feeling a little burnt out, maybe he needs to take a break and catch up with his non-physics life for a few days. If he is not having fun at all, to the point that he hates working on physics, then I'd say maybe he isn't cut out for it. Is he able to finish a calculation and get a paper out the door in a reasonable amount of time, or does he just spin his wheels and get frustrated? It's normal to occasionally get stuck, but if he can't figure out how to get un-stuck, then that's a problem.
Certainly if he doesn't enjoy it, it could benefit him to think of something else he might enjoy. Especially if it's something that pays well...