Had a similar problem with my travel trailer. Was camping and both batteries in my trailer went completely dead. I did not leave my truck connected because I realized that the trailer was pulling electricity from my truck. I discovered the culprit when attempting to leave the campsite and the trailer wouldn't move.
The trailer breakaway brake safety switch was malfunctioning and sending all the available juice to the trailer brakes. Needless to say that if I had left my truck connected I would have had 4 dead batteries (my truck is a diesel with two batteries). I simply cut the wires to my safety switch, and towed the trailer home so I could repair it at my convenience. (When I cut the wires, BTW, there was quite an electrical spark as I was connected to my truck ready to tow. This is how I realized where the problem was)
As far as being connected to 110v, however, check to see if the power converter on your trailer is functioning correctly. (This is the part that keeps your batteries in the trailer charged when plugged into shore power. Very similar to a standard battery charger.)You can usually find it by tracing your 12v wiring back from the battery. It will normally be the first place the wiring goes inside the trailer. When functioning correctly, plugged into 110vac, you should see about 14v-14.5v (With a fully charged battery) on the battery side of the 12v wiring at the power converter. If you need one, they're pretty inexpensive on eBay.
Hope this helps