Here's the real truth: Every TT sold has a built-in failure waiting to happen with the 12V system. There are things like alarms, circuit boards, radio memory, etc. that are a parasitic draw when the TT is not connected to shore power. The remedy is to either install a disconnect switch or disconnect one of the battery terminal connections while in storage.
If you just replace the battery and don't connect to shore power 24/7, you will have a dead battery again. I'd suggest to call the dealer and the Mfg, ask them why a disconnect switch isn't installed.