Outlook 2010 configured to get email from a Exchange 2007 server was prompting for credentials every time it was 1st opened, even when on the LAN. This 1st happened after the users domain password was changed.
The problem was found to be cached passwords on a Windows 7 laptop.
Open Control Panel > User Accounts > Manage Your Credentials > Look under Generic Credentials.
Edit: MS.Outlook:username@domainname:PUT and change the password.
delete anyother entries for that domain . open outlook and reenter your username and password.