Do gamepads always deteriorate from extended disuse and is there anything to be done about it?
It depends on the quality of the device, but some devices might detoriate over time, as the springs lose their strength.
However, most of the time, the cause of detoriation during storage can be traced back to improper storage for extended time.
When gamepads are stored, it is not uncommon to find the stored "upside-down" or below other stuff. In both cases, there is a continues force applied to the joystcks which strains the springs unequally.