This might be to do with your router.
If you used Port Forwarding to open the ports iChat uses you may have had to Point them to an IP address (Computer).
However if you left the router issuing IP addresses via DHCP then the computer may have changed IP, causing the Port Setting not to be pointing to the computer and it's current IP address.
Using UPnP in the router instead or Port Forwarding gets around this (If the device has UPnP)
Don't use both together as they conflict.
If the Mac Firewall Is On also check the Advanced button to see that iChat is Allowed. (In the List)
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