Dunno.. I've got a 16 year old TT that runs just fine without a battery and just plugged in. When plugged in and no battery, I don't leave the power on 24/7.. Just as I need power to the trailer for whatever I need power for at the time while it's being stored.
My batteries tend to grow legs and walk away if I leave it on the trailer, and it's parked next to my house.. I even have a video camera on it, but since I don't check to see if the battery is there or not every day... Hard to pin point when the legs grew??
Good luck!
Mitch