I too am unable to use the invite on messenger feature on Outlook.com.

When I click "Invite to Messenger" on people.live.com, and type in their email address and submit, all I get is an error saying "This Page Is Temporarily Unavailable. We're sorry, there was a problem showing this page.  We experienced some technical difficulties retrieving the content."

I'm actually trying to re-invite a contact after we deleted each other since we were unable to see each other online anymore. Now the problem just got worse because now we can't even re-invite each other.