Looking at the following document http://support.apple.com/kb/HT3774 pointed me to the right direction.
In System Preferences, Energy Saver, deselect "Wake for network access". Voila! Now the problem is gone.
Do they appear as "idle" or "disabled/asleep" on the server?
I think you need to tweek your timeouts using the terminal, then reboot server.
Paste this into Terminal and see what you get?
serveradmin settings afp
These are the commands for setting timeouts, with the number of minites at the end of the line
afp:reconnectTTLInMin = 30
serveradmin settings afp:idleDisconnectTime = 10
serveradmin settings afp:clientSleepTime = 24afp:recon1TokenTTLMins = 10080You can google for more info.