I make a lot of herbal teas that I let steep overnight, sometimes I make them in the afternoon but typically early evening. It's not usual but I have on occasion gotten busy and strained it over 24 hours later.
You do need to refrigerate it if you're not going to immediately use it all but it *should* be usable/good for the first day. This will partially depend on the conditions its in.
To my knowledge there's no hard and fast rule for how long it will continue to be good. I can always tell when my teas go bad by the taste, there's a point between good and about to be bad that has a distinct flavor but I'm not sure I could adequately describe it. I can generally keep my teas in the fridge for a week but I usually drink them all before that.