I cannot disconnect the chassis battery on mine. If I do, it sets off the Viper alarm system. So I leave it hooked up all the time.
My chassis battery used to run down in a week or less if I didn't start the engine AND drive it for about half an hour. But after the Mercedes dealer replaced the battery under warranty, it has no trouble going a week or two between charges, even with the alarm system activated..
When Airstream was doing the conversion, and while it was sitting on the dealer's lot waiting to be sold, there's no telling how far the chassis battery might have run down. Don't assume that just because you bought the vehicle "new" that it had a new battery. That battery was probably a year old by the time you bought the vehicle.
Have your local Sprinter dealer check the battery. If it's bad, they'll replace it under warranty.
Even if they don't replace the battery, bear in mind what I said earlier about having to start it AND drive it to charge the battery. Letting the engine run at idle means the alternator is turning at minimum RPMs as well, and it's not as efficient at charging that way. You have to get the engine RPMs up for proper charging through the alternator.
Engineering: Finding complex solutions to simple problems you didn't even know you had.