12V battery not charging when attached to shore power

What are the actual voltages you're seeing? You should have somewhat over 13V from the converter--around 13.5V if it's a single stage converter, something between 13.2 and 14.x volts if it's a multistage converter depending which stage it's in. If you're only seeing 10 or 11 or 12 volts, it's not operating properly and you're just seeing the battery voltage. It may be broken, or it may just be that the reverse polarity fuses are blown.