By not working, what do you mean? Is there an error message, is the page blank, are you logged in but just have to force a refresh to see that you're logged in? Clearing the browser cache by ctrl-f5 - are you doing this before you attempt to log in via FB or after?
Please try temporarily disabling the System Cache plugin, any caching options in Global Configuration area, or any other plugins for caching such as JotCache to see if this helps.