I've played FFXI for a few years now, started on the PC, and always been on the PC. I've rarely had connection issues (unless related to server maintenance or charter themselves having connection issues locally).
I purchased FFXI for the 360 (It was cheap, and I thought it'd be fun to play with at night when I'm sitting in bed).
Unfortunately, after installing and downloading the update (which itself was full of connection problems), I get disconnected from FFXI while playing on the 360. I don't have issues on the PC. Both are set up on the same router, both are wired connections.
I'm wondering if it's related to my Xbox Live connection? I notice that at night, and especially at night on the weekends, I disconnect from Xbox live very frequently. (Peak usage problems, probably?)
Does your FFXI connection rely on your Xbox live connection? (If you disconnect from Live, you DC from FFXI?).