I have a 2000 E450 that would go dead after about 3 weeks if it was parked and unused. I found that the coach builder tied a number of monitors including the steps (if yours retracts when the key is turned, it is tied in)to the chassis battery. This slowly drains down the battery.
Many others have found the same thing.
I keep the MH at home and plugged in.
The inverter does NOT charge the chassis battery. It was made that way.
So I pulled it wally world on the wed and ordered a small battery charger
http://www.walmart.com/ip/Stanley-2-amp-Battery-Charger/14560006
This plugs into the dash power outlet and into the house 120v.
No dead batteries for the last 2 years.
A search will show this is a frequent topic.