Not counting severe illness (ten days, winter of 2000-01, and thank the gods I had a live-in girlfriend at the time to watch over me or I would surely have gone mad or dropped dead from malnutrition weakening me further against the infection)...
I'd say three days. Maybe four. At some point I have to go out and buy supplies, so even during a self-imposed exile from social contact (like, say, now---between my last final exam and my first class of spring semester I've no intention of seeing anyone. Not going on any dates, and my friends are used to this from me once a year for five weeks) I'm not in the house for more than 24 hours uninterrupted. Man does not live on pizza alone and the burger joints and taco places don't deliver.
And yes, when I say "exile" I mean it. Once a year, on winter break, I seal myself off from human contact and recover my sense of self, usually aided by the Steam holiday sale.