You have used one of the links from a Document about iChat to post here.
The Document is about the Requirement specs in OS X 10.5 or iChat 4 in Leopard.
From what you post I presume you are using an AIM name.
With iChat Open go to the Preferences > Accounts
In the "Account Info tab" deselect the box that Enables the Account to Log out.
In the Server Settings change the port to 443 and deselect the SSL option.
Re-enable the account.
If No SSL and port 443 is more Stable you can try Enabling SSL again.
Most likely it is the AIM SSL server
This loses connections more frequently than the NON SSL server and iChat also need sa manual reset to reconnect when it has lost the SSL login.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously