To better help you, you’re recommended contact our built-in support: Please confirm with Office 365 admin if there’s recent change made on your account, and also confirm with other uses in the same organization to see if they are having this issue.
If convenient, use a different account, like live account to see if this issue can be reproduced, if this issue can be reproduced with an personal account, then it is mostlt related with this specific client. On your android device ( please note that this way all the cached Outlook data will be removed, please back up your important data before clearing), then restart your phone and run Outlook, and then monitor it to see if this issue would occur again. I’d suggest you to change a different network environment to see if it can make any difference. From the issue symptom, it seems that Outlook android app keeps signing out your account and asking you to authenticate.
