It would help to know if you are using iChat (where this post has ended up) or Messages.
Your specs and and Tags suggest you were not aiming to Post this in the iChat Community and that it might be related to your iMessage account (Hence Linc's response)
Messages in Mountain Lion can do Video from Buddy list like iChat did (does) or it can invoke FaceTime if you are having a conversation using iMessages with someone.
However you mention Buddies which would be AIM and Jabber contacts.
First I would check the Mac's Firewall. (System Preferences > Security and Privacy > Firewall tab)
If ON then go to the Options button and check it has "Alllow Signed Software" ticked and that Mesasges and IMAgent are in the list. (if not Add Messages and the System should add iMAgent for you when you start the app.)
If it is not the Mac's firewall it ios most likely the settings in the router you have.
Some methods of opening Ports require that the computer stays at the same IP address.
If the IP of the computer has changed then the router maybe opening the ports but listing a different IP address.
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
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