I've since observed a difference between Whisper windows:
If the other person is not on your Friends List, the window does not close when the person logs out. Of course, you also don't receive a notification.
If the person IS on your Friends List, that is when the window closes at logout.
If the other person is not on your Friends List, the window does not close when the person logs out. Of course, you also don't receive a notification.
If the person IS on your Friends List, that is when the window closes at logout.