I had the same problem exactly. While I was running the truck, the battery would charge, but on shore power it would not.
While plugged in to shore power find your 12 volt wires coming out of the converter and touch them with your finger. Wiggle them and see if the lights suddenly turn bright. In my case, the white wire coming out of the converter was quite hot, the lights flashed when I wiggled the wire up to bright.
It was totally a loose wire connection and nothing else. Sure changing the converter would fix it, because the wires are removed and then replaced and tightened. But all I needed was a screwdriver to fix mine.