OH, FFXI! I love that game, but I quit...spend a little too much time on it time to time(23hr). It's too addictive. Anyways back to your question, I am not too sure how to handle it, cause I didn't have any log on account... but it seems like this person have the same problem as yours
How to stop auto logout!
hopefully this can clear your problem up. And Enjoy Leveling!