If you want to make it so you never appear idle on anyone's buddy list, first bring up your AIM Preferences window by clicking the preferences icon in the Buddy List toolbar

or by right clicking your system tray AIM icon.

Now select the "Privacy" category on the left hand side, and then uncheck the box that says "... how long I've been idle".

Now your screen name will never dim "Idle" even if you are away from your computer for a long period of time.