I do not know if it is fully fixed since there are sometimes hours without problems and sometimes only new password prompts and no authentification possible.
But you can try this:
Make sure that you have switched on two-factor authentication in the relevant account. If you already have, please also set up a new app password (if Nine does not support 2FA for microsoft accounts). Then try to newly set up your account (delete it first and then try a fresh set up).
Try to set it up as:
- EAS with server outlook.office365.com
- EWS with servers m.outlook.com and/or s.outlook.com
Try all this with both, WLAN enabled and disabled (so only mobile network)
It could be that this will fix your account since I guess that its not only a problem with their servers but also with some accounts or some account status on their servers.
BTW: For me since today morning all works fine with my account set up as EWS with 2FA on and App password. But I did not leave my WLAN for today, so it could be that I will still get errors later on. :-)
Edit: As I do not know Nine at all I do not know what this app/programm supports but after skimming the website, I think that at least one of the protocols mentioned above should be supported.