Outlook prompts you when it can’t authenticate to the mailbox using the credentials of the locally logged on user. To fix this, log out and log back in with your own username and password. This is the fix for it 90% of the time.
Be sure you have applied the latest patches/updates to both the Outlook client machine and Exchange server.
When it gives you the prompt, do you input domain/username? or just username? Try adding the domain first and see if it works. Check your security settings too and see what the authentication method is set to. Go to tools, account settings, change, more settings, then click the security tab. Is it set to always prompt? And is it set to negotiate authentication? If it is set to always prompt, uncheck that. If it is not set to always prompt then how are you logging into this pc? Are you logging in as the domain user of the mailbox you are opening?
Click start > Run then type “control keymgr.dll” without the quotes.
Then find the entry for your exchange server and delete it. This will prevent windows from trying to use a stored password to log into exchange and use the current credentials instead. I just had this problem.