I, too, am having this problem using OS X 10.10.4
Nothing has been figured out yet.
I had a problem with FMS14 installed on 10.10.3
New Hardware,Headless Mac Pro, Pegasus2 Thunderbolt Drive Enclosure, fresh download of 10.10.3 to make a USB Install drive.
Mac Pro boots from the Raid Volume on the TB.
Everything installed perfectly as per FM install guide, FMS hosted the database flawlessly for about 6 weeks.
Then I began to have issues with FMP or FMGo clients unable to find the host. I wasn't able to connect to the Mac Pro via Apple Remote Desktop but a reboot of the Mac Pro would have everything up and running again. There were no errors or warnings in the FMS logs.
The crashes became more frequent (daily and then every couple of hours) and I began to examine the OS X system logs after the forced reboot and discovered that prior to every crash there were a lot of "FileStatsAgent[xxx]: Metadata.framework [Error]: couldn't get the client port" entries in the log. Strange that! ... this is a spotlight error and I had disabled spotlight through the command line as per Filemaker's suggestion in the install guide.
So in a effort to prove or disprove this as my source of the problem I re-enabled spotlight and reset the spotlight index with the terminal command
sudo rm -rf /.Spotlight-V100
sudo launchctl load -w com.apple.metadata.mds.plist
I was unable to exclude the FMS data area from spotlight using the privacy in the spotlight settings in the system preferences. So I decided to just let it do it's thing.
I had 1 kernel panic (new issue, un related) that evening and the system rebooted and has been stable for about 4 weeks now.
I'm not saying this is your issue, but it might be something to exclude from your fault finding.
That certainly sounds plausible to me. I did not shut down Spotlight on our original install. I will test shutting it off now. If that does not solve the issue, I will try your suggestion of deleting the index and having Spotlight start over.
I would check your OS X system log using the console utility in the utility folder to see if you have any of these FileStatsAgent[xxx]: Metadata.framework [Error]: couldn't get the client port"
before you tinker with the spotlight.
In my case I had this error repeating every 30 seconds before a crash.