I've gone multiple days without sleep quite a few times before, whether it was due to school, work, or other issues - 72 hours is about the max before you start to randomly shut down. As long as you take precautions - hydrate, keep long-term energy supplies high, avoid short-term solutions like caffeine and sugar - you can work at a relatively effective level.
Much of it is mental, and also quite a bit is preparation, at least in my experience. As far as working, I've done 25 consecutive days, but have never even neared Rudey's 120 hours - I think the most I've ever logged was around 80 between the lab and bartending.
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