I see several forum posts a month where users struggle with various ways of trying to get Dynamics CRM or the Dynamics CRM Outlook Client to stop prompting for the user’s name and password when logging into CRM or opening Outlook with the Outlook for CRM Client loaded.  This article posted by Microsoft describes several possible reasons for the behavior and provides the potential fix for each. 

Hopefully one of the resolutions will provide you with the fix needed.

When you open Microsoft Dynamics CRM or Microsoft Dynamics CRM for Microsoft Office Outlook, you are prompted for your user name and password.