I had a problem like this a while back. FM Server pings the clients about every 90 seconds to make sure they are still connected.It turned out the Firewall/Router was interfering with that ping. I don't remember what function of the firewall effected it but i could check if you can't figure it out.
This could be some form of hardware issue on the network. Things to check include the server's network card. Check the log for errors. The switch the server is connected to and the router. The issue is affecting all clients, so it has to be an area that can affect all connected clients. So it won't be the client computers. It could also be the network cable going to the server.