I also need to say that the server log shows that the clients stopped communicating. I don't know what that would be.
Beach Balls mean the machine is thinking, or looking for something.
Unfortunately, I have not yet found a way to Log what OS X is actually doing at that moment
I have one office using FMS 10 that gets periodic Beach Balls, for no apparent reason
Ping your Network connections
Run a Consistency Check and Recover, and look for "problems". "Sliding thru records" can crash if one record is corrupt
> Once the file comes up the speed is fine until I get the spinning beach baall and then dropped.
You can get extremely good clues from activity monitor and the console.
Looks like your network connection is shaky - probably the WAN connection.
FMS and FM Pro do continuously exchange data packets over the network. If the connection drops, the client disconnects.
Are you accessing the FM database over the WAN? Do you see a difference in stability if the database is accessed from a client within the internal network or over the WAN?
As gdurniak suggested, test your network with ping (in About this Mac > More Info ..., then menu Window > Network Utility)
Also, on the server, check the energy saver settings in System Preferences: Set computer sleep to never and remove tick mark at "put hard disks to sleep when possible".
I thought it was over the WAN but I tried it from a machine on the inside of my network and had a similar experience. That bewilders me. So will need to do some more testing using the recommendations given earlier, watching the activity on my Activity Monitor as well as the console. But I love it when it works.
I will follow your other suggestions as well.
We have a new Mac Pro as a desktop and have noticed a few networking-related items that might provide some insight into your issue.
Power Nap and waking from sleep seems problematic. About 45% of the time the Pro will reboot overnight claiming that it couldn't wake up. Turning off Power Nap seems to have reduce the problem by about half.
Time Machine fails about 80% of the time. The Pro refuses to see or be able to reconnect to the local Time Machine server on our network, even after resetting the account.
Apple Remote Desktop from the Pro also fails for the local server, though the Pro seems to be ok when going over the internet to another server.
We do maintain a shared iTunes library as well, which the Pro also frequently loses connection and refuses to rejoin until after a restart.
These issues are unique to the Pro, we have a number of other machines on the local network that don't exhibit any of these issues. I don't know if you're running OS X Server on your Pro, but we do know there are issues with our Mac minis on 10.9 with Server that FMS13 won't function correctly.
I responded because it seems like the networking issues we've experienced could be feeding into the problems you're having. Could be that a patch is required to resolve both of our issues.
Check if you have any external data sources defined with an IP number that cannot be reached.
You would see the beachball for a while but eventually this would time out.