The Original Poster said they were using Snow Leopard and therefore iChat 5.
For some reason this does seem to happen to AIM names.
There tends to be two fixes.
1) deleting the Account/Screen Name in iChat and then re-adding it. (the refreshes trhe Login at a very deep level)
2) In iChat > Preferences >Accounts untick the box "Use this "Account" (Log out)
In the server setting tab disable the SSL option
Log back in again. Sometimes AIM have issues with there SSL server and you need to manual reset iChat.
8:08 PM Tuesday; March 27, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.3)
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