Jack,
Again, thanks for taking the time to respond, I will test to check .
Beetle
If you change NOTHING, compared to camper at rest and unplugged from houes/shore power, when you hook to the tow vehicle, then IMHO, You have a problem, with trailer up through vehicle wireing IMHO. This is hard to think otherwise, as long as what you have todl us is true, no fridge turned on, etc. Plus you would think TV would charge battery while driving.
So if, Like you said, battery stays charge when not connected to TV, and or shore power, this means possibly someone could have moved the wires around in the connector? if they did thier own TV wiring, instead of following pinouts, which I have seen done thousands of times with 4 wires setups. Maybe TV has non stock wire setup, again if not factory there is the chance someone guessed at it... Sure less likely but possible, if nothing else maybe Tow Harnes on the Vehicle side has rubbed through a wire coating, or Ive seen them routed wrong, and got smashed enough that 2 wires touch or something is touching the frame (which is ground). Plus make sure ground is good, it wont charge well without ground, even though most trailers get "some" ground through the ball...
Good luck, I would think, Even with all the lights left on, the battery (single one) should be fine for several hours while traveling, hell I have boondocked for 2days one nite without helper/recharge power, and still life the roof up at least enought to get it down off safety...
Third thought, check battery voltage at rest unhooked from EVERYTHING, everything off and fully charged up. write it down, then hook to TV, check battery voltage again. While you connect the wires, be sure to feel the connector's wires, IS anything like your wires, getting warm? THen go check battery in trailer again! IF voltage drops, from faulty connection, or something, that is dicharging battery, and it should be evident right then. I dont know how long you travel and then discover that the battery dies when you get there, so less travel time, should be bigger drop in voltage when you hook up to tow vehicle...
Another thought, if you have shore power helping the battery(s) when you lift camper, the battery could have a weak cell, and it is getting just enough help and charge to not notice. I take my battery to Autozone, have it checked for starting power, since this is what you are technically doing when you lift the top, running a starter motor with significant resisstance, like an old hard to start pickup, so to speak...
Good luck checking things out. let us know what you find, most people never report back that something is fixed, and we read the posts forever wondering what if? LOL