Recently I had a kid and got to experience the sleep-deprivation effects all over again except this time with one big difference: I work with an awesome team who were able to pick up the slack, and I was smart enough to know when to ask for help (once literally saying "I'm too stupid to do this now, can you do it?")
Sleep-deprivation is going to continue to be endemic in our industry (not just amongst start-ups, the twenty-somethings today are going to be having kids soon themselves). Instead of fighting through the slack, find ways to mitigate it; build your teams with people you can rely on to cover you when you're short.