I am certainly no expert in this area, but can offer what little I can. First, unless something has changed from my 2016, the Chassis battery does NOT charge while plugged in. Only the house (Coach) battery(ies) get maintained while on shore power.
That said, I put mine on a charger or run the engine monthly and that keeps it up. 5 to 7 days, that is definately not right.
A good auto electrician could diagnose this at least to the point of confirming the draw (amp load test with multi-meter) or you could do it yourself. Unfortunately, the mechanics at the RV dealer may not be expert in electrics (I know mine weren't). If you or a friend is willing, pull the positive lead on the battery, set your multi-meter to amps, and make sure the leads for the meter are correctly set. Record your reading, but I would guess the draw should be very small, maintaining some LED's and computer memories and such.
The only other thing you could do to eliminate your suspicions is to pull fuses for the suspect items and see if that changes the draw down. It is detective work for sure.
Bottom line though....it is under warranty and if this dealer is not getting it done, call Jayco and find another dealer with a good reputation to fix it.
2016 Jayco GreyHawk 31DS
2016 Jeep Cherokee Trailhawk Toad.
SE Washington State