Battery can "last" several years, how soon it will discharge in storage is another matter.
The term Parasitic Loads means different things to different people, but with only some electronics on standby - I won't comment here on 0.5A trailer radio on standby - there shouldn't be enough draw to discharge it from Full to near dead in 7 days. Something is wrong - bad battery, abnormally high parasitic loads, or something else.
Things I don't understand:
1) Why disconnecting shore power in storage/maintenance mode?
2) Why disconnecting solar at all?
3) Unless it's a very modern and expensive rig with many electronic gizmos that HAVE to be either On or on Standby standby at all times, why keeping loads On? You don't need a propane sensor when trailer is locked and propane valve shut off at the tank. And, if you are keeping some loads on, you can't be sure that only propane sensor draws current. Turn the loads off, physically disconnect the loads from battery, leaving only solar charger running.