Others will have different opinions, but I believe that if you use yours once per month, you won't have any problem with your batteries without keeping it plugged in. They won't self discharge very much in a month. Of course, you must have no drain from your trailer. Turn off the battery disconnect if it has one, or remove the negative battery terminal. There are some parasitic drains that you may not be aware of. This varies from RV to RV.
Unless you have a 4 stage convertor that is designed to maintain your batteries during long periods of non-use, I'd recommend that you don't keep it plugged in. The basic convertors like the one on our Sunseeker don't do a good job of it, and can overcharge the batteries. If you can plug it in, just do it a few hours once per week. If it makes you feel better, put a battery tender on it, but I don't think it's needed.
If you can plug it in the day before you go on a trip, your batteries should be fully charged when you leave. You'll want to do that anyway to cool the refrigerator.
I live in upstate South Carolina and our Sunseeker has been in storage up to four months over winter with no battery problems. Of course, where you live there is no chance of the batteries freezing, even if they were low on charge
2011 Sunseeker 3100
1997 Pathfinder Toad