Hi,
Having read everything that is categorised as "Messages" in the Mountain Lion Community and the ichat forum as well I am aware of blips now and then in some problems being reported.
In the case of Facebook it seems to be happening again.
My reading has led me to believe that you can login in a Browser and do most things such as "Chat" (As Facebook calls it) once "Chat" has been enabled.
It seems secondary browsers (possibly Mobile Devices or a different computer) have been issues from time to time in the past.
The last time Facebook seemed to be having problems was the resetting of this browser thing which seems aimed at multiple logins.
As it was a "Security" thing as far as I could make out to set the Facebook Setting to allow Multiple browser from what people said about what they had to do to sort it - I had presumed to ask if it was similar setting this time.
My personal view is that the Multiple Browsers or multiple Logins issue also effects other apps that could login for a Jabber based chat client app (not Just Messages but say AdiumX on a Mac or a Jabber app on a PC)
On one hand Facebook appeared to be allowing access from the Mac OS and from iOS apps but then seemed to have got concerned about the issue and lack of security of multiple logins or at least access.
It would appear they are now moving in the other direction without informing their user base.
8:53 PM Thursday; April 25, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously