mid-queue Error 2002 is a combination of several questionable decisions made in the networking implementation of the FFXIV client and server
the tl;dr, here you go: The game client is voluntarily closing a healthy connection every 15 minutes, forcing you to (invisibly) re-connect to the server as though you had just pressed the ‘Start’ button. When this happens, if the login server arbitrarily decides not to let you in, you will see Error 2002 and have to close the client. Even if you have perfect network conditions in your home you will still get Error 2002 randomly and there’s nothing you can do to prevent it.
Questionable decisions indeed.