When you say chassis battery, I assume you are referring to coach or house batteries since you later indicate "engine battery" holds a charge. Is that correct?
Typically, the battery disconnect for the coach batteries is disabled when plugged into shore power. If it is actually disconnecting the batteries while on shore power, that would explain it. The batteries can't charge if they are disconnected. You would still get 12V from the converter to power things in the RV, but the 12V wouldn't reach the batteries to charge them.
As you indicated, engine battery is not usually charged by the converter from shore power.
The stock converter charger on most RVs does a poor job as a long term battery maintainer. They usually overcharge the batteries if left unattended for long periods of time. There are various solutions to this. One solution is to replace the converter charger with a better one, but this is usually only cost effective if you use the RV full time or have a bad converter that needs to be replaced anyway. Some people put the RV on a timer that only powers it up for a few hours a week. However, I believe the best solution is to not power the RV at all during storage, but add a battery tender maintenance charger designed specifically to maintain the charge without overcharging. With this, you would leave the RV unplugged, disconnect the batteries, and connect the maintainer directly to the batteries.
If the batteries aren't getting charged at all, they will eventually self discharge. There are often some items that remain connected even when the disconnect is set to disconnect the batteries. The gas and CO alarms are sometimes wired this way. If that's the case, the batteries will drain much more quickly than just self discharging.
Current RV Information: 2018 Forrest River Salem Hemisphere 282RK
Previous RVs: 2004 Fleetwood Bounder 32W; 1999 Four Winds Five Thousand 21RB; 1986 Allegro Bay 27'