I can't think of one valid reason a company would close down an mmo like ffxi.
Cheap to run, cheap to produce content for and a large playerbase (by most mmo standards).
No matter what FFXIV does it has no relevence to FFXI, they are pretty much now hitting different audiences. They would do more damage than good by closing down a game people still like and play, especially JP players. Did you see the rage and hatred to the publisher when they closed down city of heroes? Even players that don't play FFXI anymore would be angry at Square for closing down an mmo they have such feelings for as they do with this one.
Anyway to answer the question, once you see development stop it has a few years left at that point. A company that has put an mmo out to pasture is one they stop spending money developing. Since it still gets regular updates it has many many years left in it. They will close it down when it doesn't have enough players to sustain its cost. Most mmo titles run and are profitable with 2-3 servers.
FFXIV players should be more worried honestly, since that game is now seemingly not profitable enough to sustain itself without the desperate move of adding a cash shop (Selling mounts for $25 lol). Something FFXI has run just fine without for 12 years now.