This is a glitch error that I've had happen to me many times. I Googled it to find source material and ended up with the 2 threads below. I've never had this error last more than 3 to 5 minutes. Usually I try logging in one of my mules to fix the problem - sometimes that works sometimes it doesn't.
What is happening basically is that the Lobby Server has it's wires crossed. You might have just DC'd or did a force DC for some reason....or simple logged out and quickly logged back in. The Lobby Server for some reason is glitching and showing your character still logged in and if it shows your character logged in and you try accessing it, it's going to assume that you are a hack trying to illegally trying to log into the account while you are logged in. And that can actually happen.....I'm going to have to take the 5th as to why I know that this works, but it does. Also if you are online and someone else logs into your character while you are logged in, it can cause you to DC...again taking the 5th. :=) But the accounts of this lasting for an hour in the thread below surprises me, but hey, it's tech it can do weird things.
So your options are the following; Wait a few minutes and try logging back in. If you have a mule, log that character in, wait 30 seconds, log down then try your character. I've placed for you to contact FFXI if it comes down to that...contacting a GM in game will do no good, as mentioned in the thread, because they have been discontinued.
https://support.na.square-enix.com/contact.php?id=20&la=1&p=2&c=3&sc=18 - Customer Service
http://www.ffxionline.com/forums/showthread.php?t=72614 - Forum Thread