If you keep getting a recurring message from Outlook asking for some information in keychain. You may need to delete some keychain entries and relaunch the app.
It just involves telling Outlook who you are again. Follow the steps below to get this fixed and start using Outlook again!
Method
1. On your Mac, fully quit Outlook and any other Microsoft apps you have open. Long-click on the app icon itself to bring up the menu giving the option to Quit
2. Search for "keychain" in Spotlight (magnifying glass) and launch the Keychain Access App and click on Login (top left).
3. Search for “Microsoft” --> Select all entries and Delete (press the back space button to delete)
3. Then search for “Outlook:” --> Select all entries and Delete just like the previous step.
4. Relaunch Outlook app. You will be prompted to enter your Email password.
5. Once you have successfully signed in, quit out of the application and open it again. You should be able to open the app without any more prompts.