I would go to the Messages Menu > Preferences and Enable the Bonjour Account and then turn it Off again.
If that does not cure the issue have the Finder as the Front app and use th Go Menu > Go to Folder and type in ~/Library/Preferences in to the dialogue box.
In the Preferences find com.apple.ichat.Subnet.plist and Drag it to the Trash
IF that does not work delete the com.apple.ichat.AIM (or Jabber).plist depending on which service your Group chats are with.
Again restart Messages (this recreates the .plist from defaults in the app)
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