Thank you for your post, and I apologize for the late reply.
There have been no problems reported due to any Apple Security Update, and considering the number of FileMaker Server installations on Mac OS X, I seriously doubt this is the issue.
Is it possible the maximum idle time before disconnecting clients was modified?
Are all clients experiencing this problem or just a select few?
On a separate note, I would recommend updating to FileMaker Server 11v4.
I realize more than two months have passed, so if you have found a resolution, please post here so others can benefit.