Your battery could have been on it's last legs when you picked it up from the dealer. The amount of charge to the battery from the tow vehicle will be very little. Running the generator which will allow the converter to charge the battery but it takes several hours for a converter to bring a battery up to 75% and maybe over night to bring it up to 100%.
Walk around in your trailer when just on battery and see what voltage parasites you have, ie every little light is a voltage drain. Depending on how many you have will drain your fully charged battery in several days.
Make sure everything that can be turned off is. Check the storage compartment for a light that may have been left on or the light on the electric jack.
What I would do is add one more battery and a battery disconnect switch. A disconnect switch will kill everything. Your battery will stay charged for a long period of time when in storage.
A simple voltage monitor wired directly to the battery would be a good idea.
Digital Voltmeter | VoltMinder.com