According to FB's documentation on fb:login-button,

Renders a Facebook Connect login button image on your site. If the user is already logged in and has an active session, nothing is rendered (unless the autologoutlink attribute is specified).
(original from which is now a dead link as facebook wiki is closed)

However, the login button is always there, even after I have logged in by using that button.





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I confirm that at least up to now, the button will still be displayed even when there is an active session. The documentation is probably not up-to-date or it is a bug.

To get around this, simply hide it when there is an active session.



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