I have one of the old univolt systems like yours. I don't reccomend leaving it plugged up with the battery connected. What I do is leave the trailer plugged up 24/7 BUT
unplug the univolt from the 110v power. That leaves the 110v to power up the fridge (or it would if it was still in there
) run fans, small heaters, plugged in lights, charge batteries for the cordless tools, etc. Eventually (probably real soon) the Univolt will become a boat anchor and I will have the Intelipower system installed. Univolts have a history of running batteries dry, especially the older ones. When I am working on the trailer and need the 12volt I will plug the Univolt back in, typically for the weekend.