The sooner you light up a joint (or blunt) after putting it out, the better it will taste. When put out and stored properly, you can relight a dry joint from up to several days ago.
Relighting a joint is not an area of scientific interest, and as such there are no specific studies to guide the degradation of a half-smoked joint. So common sense prevails and in general, the longer you let a half-smoked joint sit out, the drier and less potent it will be.