Radio Roy, the chev. chassis uses an electric Cooling fan for the radiator. This circuit is temperature activated and is hot even with the ignition switch off. This fan does draw allot of current, the ECM is always powered to keep information stored.
Should you disconnect the chassis battery physically or with a manual disconnect switch at the negative battery terminal on the chassis battery. You will need to drive the coach a 100 miles or so before all the engine parameters are reset. This could be an issue if you live in a state that requires a computer readout to pass inspection.
By chance do you live in an area that is warmer then usual?
The other solution might be to attach a small battery charger to the chassis battery to keep it charged. I'm thinking that shore power may charge the coach battery, but not the chassis battery.
To know for sure read the voltage across the chassis battery and the coach batteries while connected to shore power.