Does it move because of rapid? Or can it lose position due to cutting force?
Have you marked the pulleys and shafts?
I recently had a lathe making bad parts because the X axis belt had broken fibers in it, thus it could stretch with load to the point that it would jump a few teeth. Just another item to check - the Z belt.
But yes it could be a loose encoder coupling in the motor or a bad encoder, or a BMDC that is not counting correctly.
If it is the SX it has the bridgeport drives and DC motors. Thus brushes to check. Newer machines had Siemens motors and drives.
George
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)