HI,
A "Certificate" to say the app has been Authenticated is placed in the Keychain as part of this Process.
As far as I can tell part of this involves the Serial Number once Messages gets to version 7.0.1 (with the OS X 10.8.2 update).
Open KeyChain Access in the Applications Utilities Folder.
See if you have an entry under the Passwords for iMessage (your Apple ID)-AuthToken
If you have then Double Click it to bring up the Info panel.
Check the Access Tab.
In here is it allowing Messages and IMAgent to access it ? (It may also list IMCore and InternetAccounts)
This could be set to allow Any app or have the "Confirm before allowing Access" option ticked.
If it is not there then open Console and try and login to the iMessages Server again and see if any messages about this turn up in the Console list.
8:14 PM Sunday; December 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