For better advice, tell us what you have for a trailer and the model of your converter. If the model of converter is known, we can tell you if it's a good converter or a battery boiler.
Off hand, one of the pitfalls of TT 12 V systems is that they come from the factory with a built-in failure waiting to happen. There are significant parasitic draws that exist (circuit boards, alarms, radio memory, etc) and they are always connected to the battery. If the TT sits in storage without the battery disconnected, the battery is drwan down to a damged state of charge fairly quick (a couple of weeks). The remedy for this situation is to install a battery disconnect switch that interrupts the parasitic draws from the battery. The above is a common cause of repeated battery failures.