On my 2007 Tour Master coach and probably on many others of that vintage the chassis batteries (for engine) are not charged on shore power...just the house batteries are. The coach batteries are charged when the engine runs from the alternator on the big diesel engine.
I added a quality float charger to my coach to keep the chassis batteries up for my long periods of not running the engine (I was living in the unit full-time...) which did run on shore power, but without that the engine batteries would indeed go flat over time.
If you have a voltmeter, you can measure the terminal voltage of each battery stack and determine which one is for the house loads (interior lights, furnace, etc.) and which is for the vehicle systems -- engine start, headlights and such.
Your coach should have two disconnect switches near the exit door marked "chassis" and "coach" (or maybe "house") which independently turn off the batteries from all loads for longer term storage. Be sure your Chassis battery stack is turned on by this switch.
Chuck
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2007 Tour Master T40C
Acura MDX toad
"It takes a great deal of time to recover from any improvement..."
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