I'm thinking it's a noise problem on the step input to the driver. Probably related to power line conditions as it's very intermittent. Since the last direction for the Z axis when cutting is down, any noise on the step input big enough to trigger movement is going to result in down motion. I'll search the forum for advice on power line noise suppression.
Hi Peter,
What you say here makes sense but, depending on your steps per unit and microsteps, you would need hundreds of individual noise pulses on the step pin just to move the Z Axis 1mm. That being the case, that amount of noise would be extremely unlikely to affect just the Z Axis.
My suggestion would be that you check all your wiring thoroughly and if possible try another LPT parallel port cable and if everything checks out OK then suspect the Z Axis driver.
Tweakie.