I had an issue where I had 2 Office 365 Outlook.com accounts configured under the same Microsoft Outlook 2013 profile that kept continuosly prompting for passwords to authenticate to the accounts.
The resolution for this issue was for me to do the following:
- Go to Control Panel. Select "View by Large Icons" in the top right corner. Then select "Mail" applet.
- Click on "Show Profiles" button.
- Click "Add" to create a new profile.
- Now add both of the email accounts to the newly created profile.
- Click on OK to save.
- Click radio button next to "Prompt for a profile to be used". Then launch Outlook and select the newly created profile.
- Verify that you are able to access both accounts under the new profile without all the pop-ups.
- Close Outlook.
- Launch Outlook again this time choosing the pre-existing profile.
- Verify that the 2 Office 365 accounts are no longer continuously prompting for password.
- Go back to the Mail applet under the control panel and change back to the pre-exising profile by "Always use this profile" and selecting the pre-existing profile name.