To clarify, the battery will normally charge when the unit is connected to shore power, and your truck will basically maintain that charge when traveling, but not much more.
If you leave the battery connected and not connected to shore power, the RV will discharge the battery in as little as a few days. If a battery is left discharged, it will be damaged, as you found out. I would have removed the battery and kept it at home when your RV went to the factory.
You should meter the voltage at the battery terminals, both unplugged and plugged in. The voltage on shore power should be above 13 volts, and when unplugged should be in the high 12s.
It sounds like the convertor is not working, and these tests will confirm it.
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Doug and Patience and Shelby the mutt
2015 Crossroads Sunset Trail Reserve ST26RB
2013 Ford F-150 3.5 EcoBoost XLT Supercab 4x4
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