Hi, I am not familiar with Sprinter chassis but some comments for what it is worth:
Some battery chargers require a minimum voltage on the battery terminals being charged before they will turn on and actually charge......so if your chassis battery is totally dead this may be the reason. You might have to boost the dead battery from another charged car battery to start your charger. Sounds like your chassis battery only charges when the engine is running (unless other methods are used). I suspect the battery isolator system under the driver seat only connects the coach batteries when the engine is running and the alternator is above 13 volts or so.......but does not work the other way when on shore power without mods.
On a side note, if you have a Fusion radio system in a Sprinter class RV it appears there can be issues when the chassis battery dies or disconnects with the Fusion system re-booting in a wrong configuration and affecting the CANbus connected systems in your coach. If you don’t have the Fusion head unit then ignore this......for those who might have one in Sprinter class coach .......see the attached:
Dead Chassis Batt now Most Sprinter Electrical Systems Fail - Airstream Forums
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