No, they didn't disconnect at the same time.  It was happening to some people more than others though. 

 

The network didn't seem slow at all.  Sometimes my post would post immediately, and sometimes maybe take a second or two at most. 

 

I'm not sure if it was actually kicking them out for inactivity, because if it removed them for inactivity...shouldn't they have to click "connect" to come back in?  It almost acted like it just said that sometimes, when a user just lost connection.  And some of them would get removed for inactivity (according to the error in the chat room), yet would automatically get logged back in.  And some people were never affected. I didn't get disconnected a single time myself.  But I saw that inactivity error a whole lot tonight for some of the other users.