When connecting to my Outlook.com account, I'm being prompted over and over again for my password. I fill it in but it does not accept it.
How can I connect to my Outlook.com account again?
This issue can relate to an account option for Microsoft Accounts, namely; Make my password expire every 72 days.
It appears that the dialog "Your (firstname.lastname@example.org) Password Has Expired" informing you about this, does not always pop-up in the foreground.
Change your password by logging on to the Outlook.com website
In order to recover, you can logon to your Outlook.com account via the web and change your password. Then go back to Outlook and provide your new password when prompted.
Disable password expiration
If you do not like your password to expire anymore, at the bottom you can disable the option; Make my password expire every 72 days
Password expiration option for Microsoft Accounts.
Still can’t logon after password change?
If you still can’t logon to your account after a password change, check whether you have Two-Step Authentication enabled. If so, you might need a special App Password instead of your regular password to logon to your Outlook.com account from within Outlook.
For more details see: Outlook and Two-Step Authentication for Outlook.com and Hotmail accounts