Hi Melanie Brooks,
Welcome to Microsoft Q&A forum.
I understand how frustrating it can be when Outlook keeps looping and asking for sign-in while you are trying to add your AOL account.
Since this is an AOL mailbox, please make sure you are using your AOL app password in Outlook, not your regular AOL sign-in password. Microsoft also notes that some IMAP accounts may require an app password when being added to Outlook.
Please try adding the account manually in Classic Outlook:
- Open Outlook > File > Add Account.
- Enter your AOL email address.
- Select Advanced options > Let me set up my account manually.
- Choose IMAP.
- Use the following settings:
- Incoming server: imap.aol.com
- Port: 993
- Encryption: SSL/TLS
- Outgoing server: smtp.aol.com
- Port: 465
- Encryption: SSL/TLS
- Username: your full AOL email address
- Password: your AOL app password
Also, please make sure “Require logon using Secure Password Authentication (SPA)” is not selected, as this can affect IMAP setup in Classic Outlook.
If the issue continues, please sign in directly to AOL Mail in a web browser and check whether you can send and receive email there. If AOL Mail works in the browser but not in Outlook, AOL recommends removing and re-adding the account in the mail app using the correct IMAP/SMTP settings.
Please feel free to let me know if you have any further updates, thanks.
Since this is a public forum, we will hide your personal identifiable information, and I have sent that image of yours containing your personal identifiable information in a private message so we can work together to resolve the issue. Also, please check your private message in case you want to share another screenshot to avoid leaking your PII by click on the Private Message button as show below

If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.