I would start by verifying the status of the batteries. Have them load tested.
Check to insure that they are getting charged by the converter and the TV while enroute to destination.
Make sure the batteries are wired correctly. One battery should have the positive to the 12 volt DC distribution panel. the negative should be connected to the other battery's negative. Failure to do so could cause the second battery not to get fully charged dragging down the first one.
Two batteries should last two or three days with the draw you posted. During colder times, the furnace will heat up the batteries.