On the 4th July 2024 I received an email from Microsoft, you might have received the same warning about a 16th September deadline. That email message included the following statement:
'If you are receiving this email, you are currently using an email or calendar app that uses a less secure authentication method to connect to your Outlook.com email account. You will need to upgrade your third-party mail and calendar app to a version which supports modern authentication methods. '
The message didn't make a lot of sense, but there was a link to web-page that explains in more details:
https://support.microsoft.com/en-gb/office/modern-authentication-methods-now-needed-to-continue-syncing-outlook-email-in-non-microsoft-email-apps-c5d65390-9676-4763-b41f-d7986499a90d
This article explains that asking repeatedly for a password is a known issue, and that after September 16th 2024 it will not be possible to access the Outlook.com account by re-entering a password.
The article explains:
The following versions of Outlook Desktop do not support Modern Authentication for Outlook.com: Outlook 2007, Outlook 2010, Outlook 2013, Outlook 2016 MSI, Outlook 2019 LTSC. Any release of Outlook Desktop with a version less than 11601.10000 does not support Modern Authentication for Outlook.com.
I think this means that after September 16th 2024, Outlook 2013 will not be able retrieve or send email for any Outlook.com accounts.
My understanding is that for my Outlook.com account, I need to find another way to manage my email, contacts, calendar, and stop using Outlook 2013 with this account, and do this before September 16th 2024!