Can Static Electricity change the voltage reference of a PCB?
Question: Can the voltage reference on the PCB be changed by wire rolling up next to a sensor? Yes it can, for example cause by ESD, however then I would expect that change to be permanent meaning a component suffered damage.

Since you can "fix" the change on the PCB by reflashing this does not appear to be what is happening. My guess is then that some event (possibly ESD) changes the content of the flash memory.

However if you have a more complex setup where a voltage is measured (using an external voltmeter for example), a calibration value determined and then programmed. Then the damage could be compensated for with a new calibration value. Probably you do not have this but I thought I just mention it in case you do.