Spike, modern bows made with glass (not all-natural or self bows) can be left strung basically forever. HOWEVER, no strung bow should be exposed to heat, like in a car or truck in the sun. They can explode. It's a good idea to break them down for transport for several reasons. This subject has been discussed numerous times here.
As far as putting it back together, yes, it might take a few shots for it to get back to where it was, because the string may "draw up" a bit. At least that's what I've experienced. Depends on the string material, too. If you make sure it doesn't untwist when you take the string off, you shouldn't have to readjust brace height when you reassemble it, once it's "shot in". Most of my experience has been with Flemish twist strings. Endless loop strings may be different, since they may not be twisted as much.