It would be helpful if we knew the model and year of your motorhome. Many motorhomes prior to 2003 don't charge the chassis battery from shore power. Most of those after that date are supposed to. If yours is a newer model you may have something as simple as a failed isolation solenoid causing the problem.
If it's an older unit as mentioned I would have the battery tested before replacing it. If it's good and just gets drained too quickly it probably has a large a parasitic load. You could also have problems with the coaches charging system.
I was in the auto service repair business many years. I can't count the number of times people went to Kmart or Sears and purchased a new battery, only to have it dead in a couple weeks. In many cases it was the result of the alternator not charging the battery, either because it failed, or the belt was so loose it slipped under load.
At the price of batteries these days I would be sure you need one, and be sure the charging and electrical system are up to snuff to avoid ruining a new one.
