Problem:

After I log out of WebMail and try to log back in later, it seems that I was never logged out and does not prompt me for my NetID and password.

Solution:

Normally when this happens the answer is that you were never actually logged out. Simply closing the window or leaving the website by navigating somewhere else will not log you out of WebMail.

It is necessary to click the 'Logout' button in order to successfully exit the WebMail system.