Stop the "don't lose access to your account" nonsense.

Not sure if anyone is looking at this anymore, but here is what we did to fix it.  We were having the prompt show up for EVERY user, not just admins.

We did NOT need to disable password self-service reset for anyone.  We just disabled the setting to force registration on sign-in.

1. Login to Office 365 as the organization admin
2. Go to Admin->Azure AD
3. Choose the thing at the top to go into the new Azure portal
4. Once in the new portal, go to Users and Groups (again, this is within the AZURE section, not in the main Office 365 admin section).
5. Go to Manage->Password Reset->Manage->Registration
6. Change the option to "Require Users to Register When signing in" to NO.
7. Save the change.
8. For us at least, the setting took effect within just a few minutes.

Doing it this way gives you the option to still allow self-service resets, if you decide that works for your organization.  Note that the user WILL still need to configure this information in their profile in order for the self-service reset option to actually be enabled for them...but at least turning off the forced registration helps with stupid users:-)

Thanks - tried that but it didn't work for us, we still have the same issue (we get the request every time that we start a new session with the portal).