http://screencast.com/t/sMlWAKsnd
Here is a screencapture of me trying to log out.
I have restarted Unity twice to no avail.
=== UPDATE ===
I even rebooted my computer and that didn’t work. What I tried next worked. I logged out of the Unity editor (not just the asset store window) and I was able to logout of the asset store and login with my personal account.