The intention of the AD Provider is to provide the user an alternative way of logging into the DNN site. Once they're logged in it's just like they've manually logged in so if they log out the cookie status is set that they're logged out and it won't attempted to automatically log them in again until the cookie expires (it's about an hour).
There is a section in the code that I inherited that is supposed to handle Logoff but is commented with a "Have to figure out why this never fires" comment. But as I think about it what are the alternatives. If the cookie is cleared when the user clicks on logout it's just going to log him back in immediately. In theory this is okay but what about situations where you, as an admin, need to login as someone else to test their account or with a host/admin user, etc. Also I can forsee calls to the admin, "I clicked on logout and it won't let me log out!!!".
In the future I'll take a look to see if I can shorten the time period down (like I said it's about an hour) before an attempt to automatically log the person in is made but if you could register this in Gemini (http://support.dotnetnuke.com) it would be great (it'll help me to not forget about it).