Constant prompts for credentials from one Mac Outlook 2011 client

There may be something off in the way the user's password is being stored in their keychain. Run the Keychain Access utility (from the user's account). If the keychain list isn't shown in the sidebar, choose View menu > Show Keychains. Select the "login" keychain in the sidebar, then run some checks:

1. Open Keychain First Aid (under the Keychain Access menu), enter the user's account password, select Repair, and click Start. If it finds (& repairs) any problems, check to see if that's solved the problem.
2. With the login keychain still selected, choose Edit menu > Change Settings for Keychain "login". In the settings dialog, check the autolock settings for the keychain; if it's set to lock after, say, 5 minutes, and Outlook checks for incoming messages every 10 minutes, the keychain will lock between each check. Generally, you want its autolock time to be longer than the email checkin time. (Note: if Outlook caches the password rather than rechecking the password each time, this will not be an issue; I haven't used it, so I don't know.)
3. If neither of those does the trick, try deleting the relevant keychain entry (/entries), and having Outlook recreate them (with the remember credentials option). Note that starting in OS X 10.9, there's a second user keychain (called either Local Items or iCloud), and you may need to delete entries both there & in the login keychain. It's possible there's something wrong with the entry, or its access policy, or there are multiple conflicting entries; deleting & recreating the entry is generally the simplest way to fix this.

Try to add an additional backslash ("\") in front of your logon domain.

Try to use:

\domain\username

instead of

domain\username

This triggers a bug (feature) in the MacOS keychain, which leads to persistent credentials.