Certainly sounds like an interference issue, which is causing the drives to trip on a fault.

Google turned up the following manual extract about what could cause issues.-
14.Protection Functions

To improve reliability,the driver incorporates some built-in protections features.

15.Over-voltage Protection

When power supply voltage exceeds +45VDC,portetion will be activated and power indicator LED will turn red.

Coil-ground Short Circuit Protection

Protection will be activated in case of short circuit between motor coil and ground.

Attention:Since there is no protection against power leads(+,-)reversal,it is critical to make sure that power supply leads correctly connected to the driver .Otherwise,the driver will be damaged instantly.When power supply voltage is lower than +20VDC,the driver will not works properly.
Where do you have the plasma wiring routed?
If it's near any of the control/motor wiring, try moving it away, even it means tying it to the roof and letting it dangle just to try it.
How have you connected the plasma cutter to the controls?

Also, you do only have the cable sheilds connected to ground at one end?