After doing the checks recommended by the previous poster, power down machine, lock it off and remove the drive. Take it to your nearest specialist drive repair center (Fanuc?).
If it were X or Y axis you could swap them to see if the fault moved with the drive.
Z axis is usually a bigger more powerful drive and on a vertical machine often has a brake circuit. (Probably not in your case).
I suspect drive transistor fault or power supply.