The same is happening to me. A good 2-3 times per full day of play. I also am having heavy lag issues.

I have reformatted my hard drive and even on a clean install of OS (Windows 7), absolutely nothing installed beyond the defaults except a browser and FFXIV, have still gotten this error.

Given the login restrictions, a crashed game can put an end to an entire day's or evening's playing. Please find a fix for this, if it's possible!