You mentioned checking the voltage with the inverter; you aren't leaving the inverter on, while it's in storage, by chance, are you?
It is possible to have a bad battery and still see 12v. I might suggest having your house battery/batteries load tested. If they load test fine, you're definitely still getting some sort of parasitic draw, while it's in storage.
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'14 Jayco Seneca 37fs
20' Look Enclosed Trailer
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