Hey Tony,
are you using the buildbotics-derived Onefinity Controller? In this case you could control it from a remote computer. This way you avoid it if the HDMI connection between touch screen and CNC controller is disturbed.
To remedy the cause you would have to avoid EMI.
There are a number of countermeasures you could take, e.g. ferrite cores, ground the machine, use shielded cables, etc., as described here.
Onefinity has this support document: