Your converter and battery may be in perfect condition, but you might have loose connections in the wiring from the output of the converter to the battery.
I had that problem. When we were driving the camper battery would charge from the truck, but when we were plugged in to shore power the converter was producing full output voltage as it should have, but one of the wires on the terminal strip of the converter output was loose. When I wiggled the wires, suddenly the lights inside the camper came brightly on and I knew I had found my problem.
If you have a visual light bar that shows your battery level you should see all lights lit up when the converter is charging the battery, or when the charging current is coming from the engine, and a good battery will show two out of four or five bars when it is disconnected from charge. If you only have one bar showing, you do not have a charged battery.
Loose connections produce heat and do not conduct electricity well, and a temperature laser gun available for about $20 would show you a hotspot very quickly without touching anything.