Every time I sign into Office 365 with my admin account, I am taken to a “Don’t lose access to your account” screen. I enter my cell number and a personal email address (because it can’t be an Office 365 account at all) and click Save and continue. I will receive an email confirming that my alternate email address has changed but the next time I log in with my O365 admin account, I’ll get the very same prompt.
Fortunately, I found some others complaining of the same issue in a thread on the Office 365 Community forums. Microsoft Support responded with a work-around to manually set the field triggering the prompt.
If you go to the Gear, Office 365 settings, and edit your settings in the ‘me’ section, you can enter your mobile phone number and alternate email there. Once those are set, you should stop getting intercepted at login with the “Don’t lose access to your account” prompt.
If you run into a permissions issue editing your Me page, you now know why the setting isn’t sticking and you’ll have to resolve that problem by correcting your access rights in order to resolve this annoyance.