Do you have a valve on your compressor to isolate it from any airlines or hoses that are connected. Perhaps the pressure in the tank lowers down due to leaks in the connections beyond the tank.
If you didn't have leak down before replacing the pressure switch and your instructions don't explain how to adjust the settings, you may be able to find more extensive instructions online for adjusting the switch to the desired on/off pressure settings.
Next step would be to suspect the check valve.
