It's a strong indication that your converter is not getting the power from the converter to the battery. Check with your meter right on the converter terminals to see if it is putting out 14V or not.
I had the same problem, and when I drove the rig, the battery would charge. After three days, the battery was almost dead while on power. I found a loose connection on the negative terminal at the converter that went back to the battery. I wiggled the wires, and everything went bright so I knew I was onto it.