I have just rerun things when the temperature is 64°F instead of 89°F. Also note I am running in air without cutting anything. I was congratulating myself because it passed the point at which I had problems before (and the motors were warm to the touch, not hot), but that proved to be premature because a bit further on the X axis stopped working again. Having tried all the obvious things at this point (e.g. unplugging and replugging all the motor connections, checking the connections between the parallel cable and the controller and between the UC100, lubing all the lead screws, checking all the v bearings adjustments, etc), I decided to try the suggestion from another post here and that was to try switching motor cables.
I decided to try switching the X and Z cables because I didn't want my gantry to get skewed if one of the Y/A motors stopped. So, I took the Red cable from the X axis and plugged it into the Z axis motor and then took the Green cable from the Z axis and plugged it into the X axis motor. I then switched the output pin assignments in Mach 3 (X became 6/7 and Z became 2/3). Checked I could jog in the right directions and then restarted the job.
At pretty much the same point (which is about 15 minutes into a 30 minute job) the Z axis stopped working with exactly the same symptoms as previously on the X axis i.e. it stopped moving as the job was running and, when I did a Feed Stop, I could jog the other axes, but not the Z. Waited a little while and then heard the "thunk" of the Z stepper (like when you first turn on the controller) and I could then jog it as normal.
As a final step, as I am using extension cables on all my axes I decided to just switch the extensions that were on the X and Z axes. This had the same result as above.
Any suggestions are truly welcome!