Try disabling App Nap if you're using OS X 10.9. Easy way is to go to the FileMaker application in Finder, then get info on the file (command-i). There's a checkbox to disable App Nap.
This significantly helped our network dropouts for Mavericks machines.
Just an FYI to the developers that although it helps to disable App Nap, it doesn't completely eradicate the issue. We have some machines that still disconnect randomly - even in Yosemite - and have diagnosed no network connection issues. The only app to suffer these dropouts is FileMaker.