At any point during studying, is it okay to just give up? Is it okay to just say "I know what I know, and I'm not gonna try to learn anymore, because I'm already so exhausted as it is"? I'm asking this because this is basically how I feel right now, and several other times, I don't know if I'm even gonna make any more progress. Has anyone ever been in a similar situation? What do you end up doing? What would you recommend?
If you cram right up to the moment of the exam you will probably perform sub optimally. You will probably remember only what you studied last, not what you learned overall. Give your mind and body time to decompress before the exam. A day might be appropriate. Your mind won't quit working just because you aren't trying to drive it unmercifully. 

In general, take regular breaks if you have a long study regimen such as for a qualifying exam. An hour or so every few hours. Use some physical activity to get your blood moving and to get  you breathing hard. Then you can return refreshed to study. 

It isn't giving up. It is just using your capabilities more efficiently.

This sort of thing has been studied extensively.