I unhooked my battery to have it tested, and my refrigerator turned off. Controls went dark. Reconnected battery and manually switched refer to Gas, then unhooked again. Don't know if it ran on gas wh...
In some cases the converter will supply the needed voltage to keep 12v appliances working. If your battery is low due to the converter not charging it, you may have a converter issue.
If you've had your battery disconnected for any reason previously and accidently arced it or temporarily hooked it up with the cables on the wrong posts, you could have blown the fuses on the back of the converter.