I just logged in (created an account) and was able to logout without problems. However, it looks like you're using the "Automatically Log Facebook Users" in feature of JFBConnect. If you're using other Logout buttons than the JFBCLogin one, those won't log the user out of Facebook as well.. in which case, the user will be logged out of Joomla.. but then when the page reloads, JFBConnect will log them back in.
If that's the case, you'll need to update the other login buttons by adding the code below:
onclick="javascript:jfbc.login.logout_button_click()"
So, the full button may look something like:
<input type="submit" name="Submit" id="jfbcLogoutButton" class="button" value="Logout" onclick="javascript:jfbc.login.logout_button_click()" />
We're looking into ways to do this 'behind the scenes', but don't have a universal way yet..
Hope that makes sense,
Alex