While not a diesel, I have an Itasca Spirit class C motorhome, and with it plugged into shore power full time, the chassis battery will still go dead if the rig is not driven. A Battery Minder solved that entirely. You house batteries are another level of troubleshooting entirely. Good luck!
Fulltimer Class of Late 2015, with my bride, Lori.
2015 GMC 3500HD Denali DRW CC LB TrailerSaver TS3
2016 DRV Mobile Suites 38RSB3, MorRyde IS