Well, I'd again say you can't afford to not rest in those cases, if you actually need to meet that deadline.

Probably every programmer have experienced the case of "Banged head against issue entire day, after sleeping and waking up the problem was simple". Sometimes, a nap or a walk or doing something else can trigger that same thing, but you skip the whole "banged head against issue entire day" if you do it immediately :)

Well, sometimes a 15minute walk will do wonders and you are fresh and can achieve more in the following 15min.