Depends on the tea (and honestly what bag it's in as well).

My loose teas. Yes, I'll reuse the leaves 2 or 3 times (typically black teas as that's what I like).

My really nice silk bags of Earl grey, no problems for 2 or 3 (in fact the first run is so strong that I reserve it for pulling all nighters and then save the bags for normal use later. No problems using it even days later if I let it dry out well).

Cheaper paper/cloth bagged tea I don't bother with. Drink it once and throw it away. Same with some of my flavored teas (I currently have a Chocolate Puerh that just wouldn't do well a second time through due to the chocolate).