Then you have another AIM client or Computer using the same Screen name logged in.
Now this maybe a client that is not On-line but allows for Off line IMs and therefore does not Log Out when Quit.
This will re-establish what it thinks is the Buddy list and add back items you are deleting.
On this iChat you are using go to iChat menu > Preferences > Accounts and change the Allow Multiple Logins option to not allow it (You will have to log out first)
When You restart iChat you may get a message that the account is logged in somewhere else. Typing a 1 in reply to this text message will log out the other incident of being logged in.
Once you are only logged in once you will be able to delete a Buddy.
11:35 AM Sunday; March 2, 2008