Microsoft has begun sending out upgrade notices for the Outlook Connector. However, it appears that the download link given still points to the old Outlook Connector version (version 12.1).
The result is that the installation will prompt you to Repair or Remove the Outlook Connector or that after you install the version given by the download link, you’d still be prompted to upgrade when you start Outlook again.
To get rid of the endless loop, download the latest version of the Outlook Hotmail Connector (version 14.0) from the correct location;
Download: Outlook Hotmail Connector 32-bit
Download: Outlook Hotmail Connector 64-bit
Note: You will only need to install the 64-bit version when you are using the 64-bit version of Outlook 2010.
The installer should automatically upgrade any old version that you might have installed. In case that doesn’t work, uninstall the Outlook Connector manually first via Control Panel-> Add/Remove Programs (Windows XP) or via Control Panel-> Uninstall a program (Windows Vista and Windows 7).
If you are still having issues then, remove the Hotmail account from Outlook, restart Outlook and then add the Hotmail account again.