I have written a guide here on how to resolve a common authentication problem when using Exchange 2007: https://demazter.wordpress.com/2010/02/09/outlook-continually-prompting-for-username-and-password-2/
Through my own problems I have also identified a configuration problem which can cause Outlook when used with Exchange 2010 to cause a similar issue.
This is caused by a mismatch in the configuration of Exchange and Outlook.
If one is set to Basic Authentication for RPC-HTTPS and the other for NTLM authentication it will cause this problem.
To resolve this, using the Exchange Management Console under Server Configuration right click on the server providing the Client Access role and select properties. Under the Outlook Anywhere tab check the authentication methods. Make a note of how it’s set.
Then, in Outlook goto Tools > Account Settings. Highlight the account configured to use Microsoft Exchange and select properties.
Under advanced and connection settings at the bottom of the screen is the authentication setting in use.
Make sure they are the same.