Usually when the client gets disconnected it is a client related problem.
Keep in mind I am NOT talking about getting disconnected, I am talking about the client crashing to desktop (fatal error in the game application - some function gets called or whatever it can't comply to), it's not the same.
If all connected clients crash at the same time it must be a problem in the map files that get addressed by the server (or script command, or whatever) or an "instruction" from the server the clients can't handle.
So this would mean the same problem should occur when playing on your local LAN, assuming the scripts are 100% the same on client side as server side.
If it does not occur on LAN side (I never experienced a LAN crash) it must have to do with the interaction between client and server. If all clients at the same time CTD it can only be something going wrong on the server side. I mean, what are the odds several clients have a connection problem and/or file problem at exactly the same time?