I leave mine half way popped up (back end) in my garage. I can't get the full camper popped up now that I have a taller truck. I keep the door opened, etc. It sits in there most of the winter. I don't take it off the truck so I keep a battery maintainer on the truck battery and on the camper battery. No issues w/ critters yet (as far as I know).
I don't keep my camper on shore power as it only powers the refrig.