Hi there. So you're working in InCopy on a Mac, and you're opening and editing files on a server. That's the usual way. Your files would not exist on your local computer, no.
InCopy keeps a constant backup of your edits, called a Recovery file. If the program crashes then the next time you open it, it should automatically open the most recent file(s) you had open, and you should see most of the edits you made, even if you hadn't saved them.
But you're saying that the program is not quitting or shutting down on you. Is that right? What happens exactly when “the connection dropped, and I've lost all my changes” .. I mean, how can you tell that you've lost all your changes? Do they just disappear on you?
Also, are you opening stand-alone InCopy stories (ICML files), or (more typically) are you opening Assignment layouts (ICMA) or InDesign layouts (INDD) and checking out stories within those?
AM