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I am not near a manual, but I believe that the E-stop switch couples into the machine thru an optical coupler. I do not believe that there is any mechinical relay involved.
If you look in the manual under electrical circuits you should be able to find this input. I believe all the external inputs that go to optical couplers are sourced from +24 VDC. Whatever the source voltage, which is identified on the diagram, you should see that voltage at the output of the E-stop switch. Whether the E-stop is normally open or closed I do not know. You will find out if you check for voltage on its output side.
There should be virtually no voltage drop across E-stop when it is closed, and probably near the source voltage when open. Expressed a different way the voltage from common (machine enclosure) to the output of the E-stop should be near the source voltage when the switch is closed (the voltage drop across the switch when closed should be in the millivolt range), to near zero when the switch is open.
I assume that the E-stop switch is not your problem. From what you describe you have a thermal problem within the control. Could be the optical coupler or anything following this. Make sure that the fans cooling the main processor board are running. The optical coupler and main processor are in the rear cabinet at the top left.
If the problem reoccurs, open the rear enclosure, and setup a fan to blow at the main processor area, top left of cabinet. Be very careful of the high voltage in this cabinet. Keep in mind that there is at least 325 VDC, and 240 VAC 3 phase or 480 VAC present.
Ideally you should you a person knowledgeable in electrical circuits to work on this problem.