If you have a digital voltmeter remove the motor from the machine. Put one lead on the motor case and the other on the machine frame, VFD metal case or a grounded location. Turn on the motor and see if there is voltage. It should be zero. Any level of voltage leakage present from the motor case to ground indicates a partially grounded winding and could be the cause of your problems. Just so you know... a 3 phase motor will run with one partially ground winding. Unless the VFD has motor ground fault detection it will just keep working until it shorts out completely.   

If the shielded cable to the spindle is attached to ground at the inverter end and to the spindle at the other end then you have two paths to ground, one through the cable and the other through the frame of the machine. This is called a ground loop. Since the motor is mounted to the frame you should leave the ground wire connected at the spindle and insulate it from ground at the Vfd end.