How to keep Chassis batteries from dying w/genset on

I just purchased a 2006 Mandalay 40E a week ago. I had the exact same thing happen to me today. I "assumed" it was due to me leaving the inverter on for the whole trip. I was at a campground on shore power for 3 days, unplugged and drove home and my house batteries were dead. After plugging in for just a few minutes, the batteries were back functioning properly. Let me know what you find out, it appears we have the same issue.