This post explains the actual cause of the problem I believe: social.technet.microsoft.com/.../outlook-keeps-asking-for-email-usernamepassword-i-know-why-how-do-i-fix
I was having this problem with a Microsoft Exchange server mail connection. I recently created an IMAP connection instead and (so far) I haven't had a request for my password and it is bliss!
I was so sick and tired of the password prompt appearing and can't believe that no one has fixed this issue considering how many people it is affecting and frustrating.
So if your mail server allows for an IMAP connection then this may be the solution.
I hope this helps!
Dave