Should I leave my Travel trailer plugged in or not?

I recommend you install a kill switch at the positive battery terminal, then leave it unplugged most of the time. This eliminates the phantom power draws that these RV's have.

Most of these converters are very hard on batteries. Using the kill switch, I leave mine unplugged for a month or two before the voltmeter I have installed in the trailer indicates to me that I should kick charge it for a day or two, then I unplug it from shore power again.