Yep, the resettable fuse is a common cause to the battery not being charged by the converter.
You still should test the battery with a hydrometer, when not plugged into shore power.
Draining the battery down that far, could've damaged a cell.
Dan-Retired California Firefighter/EMT
and Zoe the Wonder Dog(R.I.P.)
2016 PrimeTime TracerAIR 255, pushing a 2014 Ford F150 SCREW XTR 4x4 3.5 Ecoboost w/Max Tow Package
4pt Equal-i-zer WDH and 1828lbs of payload capacity