Why do I get diarrhea whenever I don’t sleep?

If you drink coffee to help stay awake - some people actually get diarrhea from too much caffeine - so if you are drinking coffee or energy drinks to help fuel your lack of sleep, this could be the issue.  (google search - can caffeine cause diarrhea)

Staying up can put your body out of sync.  Your body can't function correctly when you aren't getting the right sleep.  This can create all kinds of issues with your body functions.  

Because your body is not in sync and straining to keep up. Are you nervous about other things as well? Do you find you have ants in your pants about stuff?

It is more likely that the "partying" is the cause of the diarrhoea