Final Fantasy is similar to the Mythos. There is no real setting but rather a number of common elements that form a pseudo-mythology of sorts that can be inserted into a lot of places.
The general fantasy motif with magic, swords, and funky retro-seeming devices (like airships) and maybe tech depending on the game, all meshing together is one with universal appeal and as such I don't think the series is likely to die unless someone intentionally decides to murder/end it as I see interest remaining high in all of those elements for a
very long time if not eternally.
The death of Final Fantasy is likely to occur only if Square-Enix dies, or is bought out entirely by someone else that has little interest in the property (for example how D&D wound up struggling when WoTC was bought out over Pokemon).
The Lovecraft referance is because of the sheer numbers of people who have written things with his ideas. The idea being that you can drop "The Necronomicon" names like Professor John Dee (I think I have it right), Yog Sothoth, or whatever elese into a story and have it come along with a bunch of implications. Even when he was writing the mythos was developed by a lot of people, some of whom he was ultimatly the editor for.
By the same token you can take things like Fira, Firaga, etc.. and use them universally between games and people know what they do. Ditto for a lot of the summons and recurring chracters (like Alexander representing a Holy power, or Shiva ice).