Here's an update.
After running for a few hours with the battery completely unhooked and running many of the interior 12 volt lights, all of the sudden all the 12v lights went off. We shut them off, waited a bit, and then turned them back on with no problem. Then the same thing happened again later.
I think the issue is definitely with the converter but maybe its a loose wire or something when it heats up under load.
A couple of people thought it might be the battery not charging but the battery tested at 12.5v, so I don't think that's the issue.
Thanks to all who have replied thus far.