This doesn't happen very often but I told myself that the next time it did, I would at least make a bug report.
This time I had a few clients open but I was sleeping so the characters were just standing in Junon. At some point, I received this error message on one of the clients. From past times when this has happened, I can say that it doesn't seem to matter whether you click on "ignore", "cancel;" or simply x out the message box- the result is still the same. The client screen goes white and you are disconnected. However, only disconnected on the one client- the rest are fine and the characters were standing next to each other in-game.