the converter on my old trailer also had a relay inside that selected between the battery and converter. didn't want to mention that because i don't think they do it that way anymore.
if u are familiar with what a home air conditioner contacter looks like, that is what the relay looks like. (in air conditioning, they call them contactors; in electronics they r relays).
anyway, if the contacts on that didn't make good contact then it wouldn't switch in the battery. if u have such an animal, u may try cleaning the contacts that are closed.
sense u aren't running slide outs or other heavy current items, ur converter may be like that.
i'm still betting on a fuse between the bat and fuse panel.
on my 1984 trailer, when u plugged in to AC, the converter supplied all the power and disconnected the battery from the trailer (relay would select). it had a trickle charger built in that kept the battery maintained.
when u unplugged, the relay would drop and select battery for the trailer.