Same problem here. I bought the game last week during the Steam summer sale and I've not been able to play for more than a couple of minutes without getting disconnected from the server. I contacted support on Friday and they advised me to change the UPnP settings in the FFXIV.cfg file, which I did. I let them know on Saturday that this did nothing to change the problem and I've yet to hear from them.
I'm very frustrated about this, everything else works just fine (other on-line games, Netflix), it's only this game I just can't play. I'm hoping for an official statement soon so we at least know what's being done and how long it might take to fix it.