I Can No Longer Access My Hotmail Account On My Android Device
Usual solution is to remove and re-add the account, on your mobile Outlook.com.
Generally that works.
(Obviously you will lose any mails and unsent outgoing mails (manually save unsent outgoing mails first with some file-manager app, if you need them)).

Be warned: Outlook.com's Android sync is very brittle, and their support is nearly non-existent.
Beware of taking over-the-wire Android updates.