You did not have these issues with 14v3? Then I would suggest rolling back to that if you are not running El Capitan.
I am having this problem as well. It first happened 12/2/15 and again 12/4/15.
I was on FMS14 ver 126.96.36.199 (Win Server 2008) and had been for a while. I updated to FMS14 ver 188.8.131.523 (latest) and did not see the problem again until this morning (12/16/15).
Looked at FMS logs and the only thing that seems common is that fairly soon before FMSE terminating, the server saw a "Scripting Error (3)" in one of the scheduled scripts (though not the same script each time. This error is a script step that is not compatible with server but the step has been in my scripts forever ;-) and is hit dozens of times each day without failing.
I wonder though if errors like these (the error 3) pile up over time and make the FMSE crash.
Who knows indeed, but it certainly would be good idea to remove those incompatible script steps or branch around them when the script is executed on the server.
Another thought is to check the stats log and see if there is a pattern of high activity around the times that FMSE fails.
What is a good way to tell if a script is being run on server? I guess I could check Get(hostname) but that seems iffy (host name gets changed).
Get(ApplicationVersion) will have the word "server" in it