Our battery in the RV went down this weekend and wouldn't stay up while running down the road. I checked it once back home, and with the switch in "Store", the battery puts out about 8.5 volts whet...
adding to my previous post on engine not charging house...
12.45V is about 3/4 capacity. assuming your house batt has a capacity of maybe 110 amp-hours, in 4 hours your batt went from 110 to 0.75x110, or 7 amps per hour.