Probably an encoder fault. It is typically inside the motor but I have not worked on one of these machines. The Z motor does not move thus the cable does not flex so I do not believe the fault to be in the cable.
There is the outside chance that the error could be in the control itself.
Swapping the motor encoder assembly with another one could shed some light on this.
Remember to support the head as typically, the Z motors also include a brake.
George
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)