The tech specs for FileMaker Server 13 do not include running on Mavericks Server!
So the issue that you have come across is obviously something that FileMaker has already tested and as yet has no solution for.
Do you need to install Server on your Mavericks machine?
It may be more robust without Server installed.
Best wishes - Alan Stirling, London UK.
Thanks Alan, but this was not FMS 13. I wrote FMS 12.06 int he 4th paragraph, 2nd line. I apologize for not making it more prominent.
This acted the same for me under 10.8 as it does 10.9 with Server.app installed. You can't have any web services enabled in Server.app as it conflicts with the install of apache that filemaker requires.
I was only able to resolve by re-installing FM Server, as you mention. Do you have all web services turned off in Server.app?