As ChrisF suggests, the pragmatic short term solution may be to use the pause and resume trick, but you have to talk to your customers to know what your priorities should be. For example:
If the fault trashes a £1000 part or causes 4 hours of downtime once a week, while the pause-resume fix reduces production by 1%, they will probably prefer the fix right now.
If the fault trashes a £1 part or causes 4 minutes of downtime once a week, but the pause-resume fix reduces production by 1%, they will probably prefer to wait for a fix which doesn't affect production rate.
Having worked in the laser micro-machining industry for many years, I know just how much pressure you can be under to optimise the process and make your machine produce as many parts per hour as is possible, so either way you are going to be under pressure to fix the problem properly.
In my experience, the only way to effectively track down a Heisenbug is copious logging. Log everything in and around the part of the code which could be responsible for the error. Learn how to read your log files effectively, make sure you are monitoring following error on your motors (are your stages moving where they should when they should?). Look at the memory usage on the machine, is a memory leak causing a critical process to be starved?
Make sure you are logging user actions too, are you sure that the operator isn't hitting the emergency stop so they can pop out for a shifty cigarette break while it's being fixed? I've seen this happen!
Also, look for correlations between scribing certain patterns and the bug being triggered more or less often. If you can find patterns that trigger the problem more frequently (or never trigger it) these may point to your problem.
Try to make patterns that trigger the problem even more frequently. If you can find a way to trigger the problem reliably then you are half the way to a solution.
Finally, don't be quick to blame the hardware, but never assume that it's perfect. Many times I've been blamed for problems which turned out to be electrical or mechanical in nature, so you always have to have that at the back of your mind.
Even though you may not normally have access to the machine, remember that some problems can only be efficiently solved on the machine. Sometimes a few days on-site can be worth weeks via remote desktop and months off-line completely. If you run out of off-line options, don't be afraid to propose a site visit, they can only say no.
You might also want to look at the questions and answers to What do you do with a heisenbug? and What to do with bugs that do not repro? but these might not be so useful for your situation.