I often re-steep previous nights tea, but again, as everyone else says, I always do a quick boil-rinse to rejuvinate the leaves. I especially do this for two reasons: 1)I am not really in the mood for a particular type of tea (so why start a new pot of something I might not finish anyway), or 2)It is really expensive tea and I want to make sure I get my money worth (though I usually dont leave it in the pot.....I will take it out and spread it on a plate and it usually dries up in a couple hours and I will throw it in again in the morning (I never dry the leaves and save them for days or anything). Honestly, there is no real harm in doing it.......doing a quick rinse-boil will certainly prevent any harm, and as long as it tastes good to you, why not? Hope this helps!
*Also, though I just started drinking Pu about a week ago, I have re-steeped some in the morning that I had the night before and I could not tell much of a difference