How to hold leaves between infusions depends on the leaves, and your local environment. As long as it's not too hot/humid, I just leave leaves in the pot or gaiwan overnight or half a day, out at room temp. Sometimes if I know it will be longer and I really really want to reuse those leaves (e.g., precious & pricey aged puerh sample), I put the pot in my refrigerator.
I rarely leave green/white tea out for more than an hour, since it's not brewed as hot as most others, and it seems to suffer more than the rest in terms of quality. Morning sencha does work pretty nicely with some cool water poured in, left in the fridge, and I get a nice cup of cool tea at the end of a hot day when I return to it.
But teas brewed with near boiling water (oolongs, puerhs), I figure just about anything I'd worry about making me sick was already killed with the first infusion or will be killed with the next infusion so it's unlikely to hurt me, and the leaves stand up to the delay better.