Hi,
To summarise then.
iChat randomly asks for the Passwords now and then.
These are in the Keychain and iChat has Access.
You own and and Read And Write Access to the Keychain.
I am also presuming you have tried Keychain Repair.
The Original Answer marked as correct suggests deleting the com.apple.*.plists which you have done with partial success.
You also Own and have Read and Write permissions to the .plist
From that we can presume, as they are being rewritten, that you Own and have Read and Write permissions for the enclosing Folders (Home folder and Library and Preferences).
This on Lion and therefore iChat 6
This means that the details also appear in System Preferences > Contacts, Mail and Calendars
You have tried deleting the accounts in iChat and Re-adding them as well.
I would be tempted to try deleting the accounts in iChat and then adding them in Contacts, Mail and Calendars to see if it makes any difference.
Also check that in the Hard Drive (the top level folder) that there is not a Folder called Previous System.
This should not store any info relating to this even if it is there, but it may provide some clues.
Did you create a Lion Disk before installing Lion ?
8:23 PM Wednesday; September 21, 2011
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
G4/1GhzDual MDD (Leopard 10.5.8)
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"Limit the Logs to the Bits above Binary Images." No, Seriously