I'm with you, Lou.

My inbox stopped synchronizing on April 3 for no apparent reason; Web-based
access to my paid Hotmail account (of over 6 years) still functions. Not much
help to be found from Microsoft on the Connector, and I'm resisting going the
paid support route for this.

I've removed the Hotmail account from Outlook, then re-created it. Then even
removed the account, uninstalled Connector, made sure ALL Outlook patches
were installed, downloaded the current Connector v12.0.4518.1068, installed
it, re-created the Hotmail account...and nada. The log says I successfully
sign-in, then I get both the bogus 4350 error, plus one without a number that
says an "unknown error was encountered," and to check the "Synch Issues
folder." But there's no longer a Synch Issues folder locally or via the Web
interface.

I've been using Connector since Hotmail went to "LiveMail" with varied
success, but never outright, unrecoverable failure. Now I'm dead in the water
and MS seems to offer no support for the product save less than a handful of
KB articles, none of which apply.