I've seen this as well, but I haven't found any solid cause. In a few instances, the client's ISP is to blame. About two weeks ago, it was mine. Check for other network outages (email or browser) not functioning.
How much RAM do you have in the mini? Does the drop occur during a time machine backup, either the server or some other computer backing up to it? Are the FMS backups triggering the problem?
These are some of the items I've tried to check, but as it's very intermittent, I haven't been able to pin it down yet.
Be sure both the server and all clients are set to never let their disks sleep.
How is these connections made: Ethernet, WiFi, 3/4G or ? WiFi's seem to often drop out for reasons of their own.... and 3/4G connections AKK!
Does your server have a dynamic or permanent IP address?
Are there any things in common about the clients that drop off as opposed to those who are OK? Hardware, OS version, etc?
Just fishing for ideas.
correction: turned out to be some kind of telnet session that was running from a machine with the same fixed IP number :-|
thanks for your suggestions. It looks like we've found the problem; clients with FileMaker Pro 10 on OS X 10.7 in combination with FileMaker Server 11 on OS X 10.7. These clients where working just fine with FileMaker Server 10 on OS X 10.6. Updating the clients with Lion to FileMaker Pro 11 solved the problems. Very strange !?
best regards - Dick