Before, I used to exhaust myself just keeping myself doing whatever it is that I have to, even if it's not yet needed for the next day. But I found it be very inefficient because the next day I am so tired and I tend to oversleep, so my sleeping pattern is greatly affected. I also feel more stressed. Unlike when I sleep and get the right amount of sleep, the outcome of whatever I do and my performance while I do it are often better. So I suggest that you just get enough sleep, don't push to the very extent of your limit.
Of course it is never really good to force yourself to do something when you are very exhausted and tired already. I can hardly think and concentrate when I'm feeling sleepy already. So we should always listen to our body and give it the rest it deserves, because we won't be productive at all if we deprive it of sleep.
I can't really do that with my sites because they start over the next day but if I'm just way too tired to go on then I know it's time to quit. if I had a regular chore to do or something that's personally important for me to do (like something creative) I definitely try to go to bed. Unfortunately that wasn't the case last night and before I knew it it was 4 in the morning.