OK, diodes can fail either open, or shorted. moving on.
Batteries with no load - disconnected - should last weeks between charges. If there is in fact no load, then you have nothing to loose installing them in storage. If there is a phantom load, a battery disconnect switch will deal with it without removing all the cables. If you put in a switch, the solar goes directly on the batteries. The radio memory in my truck goes weeks between starting it with no issues, so I think your problem is elseware.