Yes, the chassis battery will lose the charge in a couple of weeks. I found mine would be dead in a week or so. Our Winnebago c-class is parked beside the house, plugged in when not being used. Biggest draw I had was the key fob unlocking coach door which also turned on cab courtesy lights for a minute each time. All powered by the chassis battery. Another draw was the step going in and out, unless I locked it out.
About 10 years ago, I installed a 'battery maintainer' on the chassis battery and plugged the maintainer into a coach 120 vac outlet, always on when RV is plugged into shore power, 98% of the time.
Chassis battery history, 2006 MH built on 2006 chassis in Feb 06. We purchased coach new in May 2007, had been sitting on dealers lot over winter with a dead battery.
June 2007, Ford dealer replaced with new Motorcraft battery under WARRANTY.
~2010, installed battery maintainer, to resolve same problems that OP is having.
June 2019, 12yr old Motorcraft battery becoming unreliable, even with maintainer hooked up. Finally had to replace with new battery (from Costco).
Ken