I've experienced this a few times as well and I think I can answer some of Michiel's questions.
Logging out of Mendix, closing the browser or tab or typing in a new URL all cause the problem. It's not only IE 8, but also IE 7 (didn't test IE 6).
It seems it has something to do with clearing cached objects, as the time the browser is unresponsive correlates with the amount of forms you opened and action you performed during your session: logging in and directly logging off doesn't take any time, but after clicking through some menu items, you'll notice the longer log off time.
I also think it has something to do with the Mendix version used, as I seem to remember having this issue with a project some time ago and now (using v2.4.3) not anymore, but this could very well be my imagination. One project I can easily reproduce this issue with is your MXDN system, which runs on v2.4.0 I think.
Does he/she not have problems with other browsers? You could try monitoring the network activity by using a proxy to find out which request takes such a long time. This would help figuring out what the cause could be.
I have tried (and failed) to reproduce this in several projects using Windows XP and Internet Explorer 8.
The 'logout' button triggers a request to the server to invalidate the session, after which the document location is changed to the login page. If the application you are developing and testing works normally, there should be no reason that the 'logout' request itself should take a long time.
I suspect that it is the change of document location (the URL in the address bar) that is causing the problem. Various builds of Internet Explorer can be, ah, inefficient in certain scenarios when it comes to loading/unloading documents. IE seems to put a lot of effort into making sure that a document is unloaded properly to prevent memory leakage, but unfortunately blocks the user interface while it's doing that. (Not having access to the source, this is conjecture based on observation, of course).
If you can verify that the 'logout' call works as intended, we can start to narrow the problem down.
Whatever the result, it would appear that you have stumbled on an edge-case for the client. I suggest you also open a ticket in MXDN for this case.