GMail account in Outlook on iPhone

For Outlook on iPhone with a Gmail account, repeated Google sign-in prompts are commonly addressed by checking these items:

1. Update Outlook for iOS to the latest version. Repeated password prompts can happen after security standards in the app are updated.
2. Make sure Gmail IMAP is enabled:
   • Open Gmail in a browser.
   • Go to Settings > Forwarding and POP/IMAP.
   • Under IMAP Access, select Enable IMAP.
   • Select Save Changes.
3. Remove and add the Gmail account again in Outlook for iOS:
   • In Outlook, tap the account icon.
   • Tap Settings.
   • Tap Add Account > Add an Email account.
   • Enter the Gmail address.
   • If Outlook does not automatically detect Google, tap Google on the account setup page and then sign in.
4. If Google two-step verification is enabled, complete the Google verification screen when it appears. Outlook for Android and iOS supports Gmail two-step authentication / verification.
5. If the issue continues during Google verification, use Google’s two-step verification help page: this Google page.
6. If the problem is with a Microsoft account in Outlook mobile instead of Gmail, use the Microsoft sign-in helper tool: Start.

References:

• Can't sign in to the Outlook mobile app
• Does your app support 2-step authentication / verification for Gmail and Google Apps?
• How do I add a Google Apps account?
• Enable IMAP in Google Settings
• Fix problems connecting your Google account to the Microsoft Cloud