Hi,
In iChat > Preferences > Accounts > Server settings (After you have Logged out) try it without the SSL Option.
AIM had less SSL servers for the previous servers listed in iChat 4 and 5 (which could do SSL) and if there was a problem then you get kicked Off.
If you lose contact with an SSL Server in iChat you need to manually reset the Login.

11:26 PM Friday; January 13, 2012
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