Do you have Anti Virus running on that computer?
Do your have Index Search disabled on that computer?
Is it a dedicated server with just FMS?
What version of FMS is it?
You can read more in this thread:
Thanks! No, yes, yes, 14.latest and we had a similar problem in 15.latest also.
We've got fminc working on it at least another dev is experiencing the issue.
If you have Index on, then disable it right away. It might get your database corrupt.
It appears that the issue was caused by interactive container uploading/viewing/downloading by one of our user groups which was crashing their FMPro client apps. The feature had been in place for a few months though, however after we reconfigured the way it's used so that all documents are read outside of FM, the crashes on the clients went away and it seemed to mitigate the fmserver.exe kills. It's been over 2 weeks with no fmserver deaths so that's good. The ability to view files in FileMaker is huge selling point in many projects. I don't know why FileMaker Inc doesn't tighten that engine up asap.