I don't know. Focusing on school and a startup is sure one circus act that I'm still having trouble with, but staying up for two days straight is not a good idea. The best way to get things done is to manage your time well and get as much sleep as possible. I try to focus on working out, making my launch stay to one date, and keeping my grade above average. This requires me to get as much rest as possible, I sleep for 8 hours a day and I get a lot done.
I'm a high schooler, taking 7 AP courses and 2 other courses with no lunch period (I have to eat during some classes). After school, I run 10 miles cause I'm on the distance running team. I get home, shower, dinner, and between 8pm and 7am, I have 12 hours to do a combination of sleep/homework/programming.
So from my experience (as someone who averages 3-4 hours a night), NO CAFFEINE. Caffeine ends up destroying you and making you less capable of doing things. Apples wake you up more than a cup of coffee. EXERCISE. A few pushups in the middle of the night wake you up better than anything.
Prioritizing is probably the most important. I usually go Schoolwork -> Programming -> Sleep as my priorities. On days before track workouts or races or big tests, I swap Sleep and Programming as priorities.
It really is difficult to balance school and programming, but hey if you want to pursue something you gotta give it your all. Just don't destroy yourself while you're at it. I exercise, eat, and sleep binge on weekends. Its a good life.
Remember, doing all this I-am-startup-man-stuff is very much possible when you are healthy. If you start to feel even the slightest bit sick, most if not all of it goes out the window. Feeling you are getting sick is a red flag from you that one or more variables (nutrition, stress level, amount of sleep, exercise, workload, social life) is out of whack. Better, focus on balancing your life so you don't get sick (eat right, exercise, take a break and go out with friends).
I think it all depends on how one can handle small amounts of sleep. I know that I am able to go long periods of time with little sleep. I once worked landscaping for a summer and would work 15 hour shifts and consistently get 4-5 hours of sleep.
I don't think doing something so unhealthy could possibly be worth it. There will still be startups left to be founded after you graduate. Or there will still be grad programs left to be attended after you IPO.
Drop out, if its what you really really want to do. I spent three years trying to do startup stuff and school. Eventually i realized that i was really happy only when i had time to focus on my projects, and that school work got in the way of actually completing something to a really high level. Its a great way to train, but if you feel that now its time to do something serious - drop out.
This advice would be more convincing if it was from the google founders. "We never slept because we were simultaneously going to stanford and making google. Our success is due to coffee."
Instead it is always from someone working on something lame and going to some random 2nd rate school. Most people who are good at what they are doing have time to sleep.
The no sleep is tough for me. Historically, I've required about eight solid hours. Lately, I've found that with a morning exercise routine I can cut about two hours out of my night's sleep and still function fine. Anything less than six hours and I start to require a power nap during the day.
