Wow thats sounds very strange.
If we have to count with condensation from hazers and co2 fog in this case I am much more suspicious the for the cable which connects the LCD to the mainboard. (White small flat ribbon cable)
As you said “Last two shows both player stopped displaying time (but playback continued)” in this case the problem must be the display. If there’s any problem with the USB host cable the device lost the connection with the drive and the device reboots.
When you had this issue with the device is the iPad displayed the content properly?