Hello,
Which type of email account are you using? Exchange, POP3 or IMAP?
What's the detailed version number of your Outlook 2010?
You may first try clearing the credential cache for the email account from Windows Credential Manager and then start Outlook to see whether this issue continues. To do this, please follow:
1. Click Start, click Control Panel, and then click Credential Manager.
Note If View by is set to Category, click User Accounts first, and then click Credential Manager.
2. Locate the set of credentials that has Outlook in the name.
3. Click the name to expand the set of credentials, and then click Remove from Vault.
Outlook prompting for password could also happen due to several other factors. We have a forum article which listed some general troubleshooting steps. You may look through this and see whether it provide any help:
https://social.technet.microsoft.com/Forums/en-US/bcd2d9c2-1a1b-4446-bf32-69fee8cdf11b/why-does-outlook-keep-prompting-for-password?forum=outlook
Hope it helps.
Regards,
Steve Fan
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