I leave my batteries on a "really working" SMART MODE CONVERTER/CHARGER unit in my trailer all the time when sitting at home. These working smart mode unit really take care of your batteries for you.
I would become very knowledgeable how your batteries work and watch and maintain them. The batteries is your trailer life-line and will last many years if properly maintained.
If your Trailer on-board converter/charger is the single mode type unit that only puts out 13.6VDC then this will require you to keep an constant watch on your battery fluids as 13.6VDC will tend to boil out battery fluids over time. Once the battery fluid level drops below the cell cores then the battery will start building crud on them and eventually short between the cores. When this happens it is usually game over for the battery.
Also keep in mind that a fully charged battery will do quite well when completely disconnected at one of the battery terminals when in storage mode. They will hold their charge for very long periods of time even in the winter months. Here again you would want to monitor them and put back on charge occasionally to keep them topped off.
Parasitic drains from installed trailer appliances and devices electronics boards left connected to your trailer battery setup can drain your batteries rather quickly sometimes in just a few days time. You need to be mindful of what parasitic drains you have in your trailer.
The big rule of thumb for me was to never let my batteries drop below their 50% charge state which is pretty close to only 12.0VDC. When camping off the power grid my number one priority is watch my battery DC VOLTAGE with an inside mounted monitor digital meter setup. It takes planning to know what you operate when camping off the power grid and the game plan is to make it until the next morning with what you have and then recharge the batteries back up to at least their 90% charge state each so you can do this all over again for the next day/night run off the batteries.
You just can't show up at the off road camp sites and expect it all to work for you... It usually gets dark on you around 10PM at night when you first do this haha...
Camping in your back yard has a lot of merit sometimes learning how things work battery wise.
We enjoy our many camping trips off the power grid over the years the best...
Just some of my thoughts here...
Roy Ken