I just had this as well. A few google searches seemed to indicate that it's relating to the way your PC is accessing the net (rather than just the FFXI launcher).

Suggestions included resetting your router, setting Firefox as your default browser (or anything but IE) and resetting the PC multiple times, the idea being to disconnect whatever is interfering with your connection.

The first two didn't work for me, but the rebooting did. Have had a number of IE updates lately and IE has been doing weird things on that PC anyway...