It depends upon the type of converter you have in your camper if they continue to charge or if they have a turn off feature when charged, and a trickle feature when not use the camper at all.
I've had 3 different campers now: Dutchmen Sport, Keystone Springdale, and Keystone Outback. All 3 of them were left plugged in 24x7x365 from the moment I purchased the camper to the moment I sold them (except my Outback... I not selling it!) I've never had a battery over-cook or go bad.
Now my pop-up (in 6 years, when through 2 batteries) fried them up. Lesson learned to unplug in the winter. But never the with travel trailers.
