I think it would be better to figure out why the FMSE is stopping. There should be a log entry before the one you reference that describes what script caused it to stop. It's most likely a script that doesn't end and FM Server just shuts down the Script Engine.
I agree that it would be best to address the cause, but the cause is intermittent and uncommon. It is not the same script that causes the process to terminate. I am still trying to figure out what is actually going on.
My server runs two scripts every few minutes to handle specific functions. One fetches new ODBC data and runs a manipulation on the data locally to speed access in the UI, and the other finds new data that requires e-mail notifications to be sent. They are short scripts (taking a few seconds with a timeout of 2 minutes just in case).
My only thought is that it might relate to more than one schedule overlapping with the hourly backup, but even this doesn't really seem to be a common thread.
I see your dilemma. FM Server can run a system level script but it that probably uses the script engine as well?
You would probably have to setup the schedule in the OS.