server "imap-mail.outlook.com" is not responding.

I experienced the same issue, this is how I could get around - I set up a new mail acount in iOS 16.7.10 choosing ‚Outlook.com‘ following the guide line, but have chosen a different account name.

It works like a charm, I just had to change the synchronization settings to „unlimited“ (I am using the german language iOS, so I am not sure about my translation, sorry).

I started synchronisating with my Hotmail-account almost immidiate.

If you are deleting your mails after downloading from Micros*** you probably will keep your ‚old‘ outlook account on your iPhone/iPad.

Hope this might help you too.

Download the Outlook app on the App store and use that for Hotmail and Outlook email accounts

I have the Outlook app but my mail app has stopped working. Deleted and reinstalled but now can’t see any of my mailboxes and saved emails. I’m not tech minded - can I recover my mailboxes through the Outlook app? Got lots of info saved on Mail so stressing how to recover. Any help?

Is now sounds like a Microsoft - Apple problem. I am not that tech savy either, especially on the iPhone. You can try this Link to see if gives better answers to the problem. Set up the Office app and Outlook on iOS devices

Thank you - just hoping I can get it sorted 🤞

Exactly the same problem. Stopped working on my iPhone, iPad and macbook air. Really annoying. I can access it by going to the outlook website so know passwords are working fine.