I had the same thing happen to me. The converter was working hard, and the battery was not charging. After three or four days, the battery was almost dead, down to one idiot light.
I measured the output of the converter at the output terminals and it was 13.7, but at the battery the voltage was under 12.0. I began wiggling wires feeding from the converter to the battery, and suddenly all the inside lights came on bright. Aha, it was a loose negative wire from the converter to the battery.
Start there, then check all your main battery posts and the wires from the battery to the converter. You might be lucky like I was and find the problem.
If you have a laser gun thermometer checker, use it to check the connection points. A weak connection will make a lot of heat compared to a solid one.
Good luck.