Hi,
We are seeing more of this in Mountain Lion OS X 10.8.2
Before this several fixes were tried and worked for smaller and smaller groups as time went on.
First add a Public DNS server to System Preferences > Network > Advanced Button > DNS tab
Google run 8.8.8.8. and 8.8.4.4 (It may also pay to add them to your router)
Also try open the Activity Monitor (Applications/Utilities) and finding imagent (Lower Case) and highlighting it.
Then use the Quit Button top left and confirm Force Quit.
Restart Messages afterwards.
If you are still having problems type ~/Library/Preferences into the Finder > Go Menu > Go to Folder at the dialogue box that appears
In the Preferences find com.apple.imessages.bag.plist and drag it to the Trash
Restart Messages.
If that does not work delete (Drag to Trash) the com.apple.imservice.imessages.plist and restart Messages
It is also worth trying to delete them together and restarting Messages.
At this point the most likely cause seems to be an absence of the Serial number in System Information > Hardware.
It is Flashed to the Motherboard and can go Missing if the computer has the major broads replaced (refurbishments and Repairs).
It is supposed to be flashed back by the Certified Apple Technician (At the Store or Apple Authorised Repair Center).
It could be a simple check to verify the computer can run Messages.
It could be a deeper check for general security about logging in to iMessages.
9:58 PM Friday; November 16, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously