I had the same problem. Plugged in to shore power, the trailer battery charged and all was fine. Trailer lights and brakes worked fine when plugged in to the truck. Traveling for several hours with the fridge on produced arrival with a dead battery. Granted, the single camper battery was 5 years old. The RV tech checked the truck output with this:
The truck was producing the 12V on the charging line, but the camper battery was not taking it. Then he found a bad ground in the camper. Problem solved. Now with a new battery, all is well.
