Recently, my Lumia 920 stopped connecting to Facebook IM chat. I tried all the solutions being posted on the internet, including resetting the account, switching off/on the services etc. Nothing worked, then I remembered adding an alias to my Microsoft account which is being used as a primary account on my phone, to which the Facebook account also connected. The new alias what I've added has been set as primary alias. So, I thought that could be the possible problem as the Facebook service is connected to my Microsoft account with my old alias. I changed my old email address as primary alias, and checked the Facebook chat, it started working....
So, for example if you've signed up your Windows Phone with a Microsoft account (Hotmail, live, msn, etc.), after which if you've set a new alias using Outlook.com, then make sure your old email address to which the Facebook services is connected is set as primary email alias.