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Well, if the logo is coded on a page that reloads when a user logs in, or accesses a menu item, then the flash movie will play again.
Now, you *may* be able to use cookies/sessions with actionscript to only play the movie once, but in that scenario you would have to use cookies/session info based on whether the user is logged in or not.
Do I know how to do this in actionscript, unfortunately not. I started looking into it for a site I was working on but then the client decided to remove all flash - made the task a low priority.
Another option could be to use frames (yuck) or something that can mimic frames so that the actual flash movie is only loaded once, however the problem would be detecting whether or not the user is logged in.
Hopefully someone else can actually have some good advice for you.
:)