Did you re download just this mod or advanced addon as well? Any errors or warnings in your log? Single player or multiplayer or both?
Viewing post in FS22: Advanced Moisture System comments
I'll check again on my end. It was saving and loading for me when I tested everything. Is this happening just with vehicles, or with storages, or is nothing saving?
Edit: Just re-downloaded everything from here and tried again. Vehicles and storages (silos) saved and loaded correctly on my end, from what I could tell. Field moistures were also correct. You could open your savegame xml files and look to see if the entries are being saved properly. If they are not in there or are not correct, you may have some sort of mod conflict.