I didn't play FF XIII to begin with...truth is I haven't played an FF game since I rented FF X-2 and took it back approximately 2 hours later when I realized it was essentially Barbie Dress-Up in Final Fantasy Land. But aside from the fact that I'm an XBox player and as such have been disconnected from the FF series when it became PS exclusive, the last FF game that I actually enjoyed was the original Final Fantasy Tactics for the regular Play Station. I could be wrong on my dates, but I'm pretty sure that was the last one that Square Soft made before they became Square-Enix. FF8 was just way too easy, FF9 was way too childish and cartoony. Thought I enjoyed FF10, but the more I thought about it the more I realized I just liked playing Blitz-Ball, and then as I said I rented and returned FF 10-2 within a couple hours.
My personal history with the series aside, I believe the franchise has been going downhill for a long time. Seems to me that Western players just aren't into the whole image of the JRPG for reasons that Yahtzee does a fantastic job of illustrating (the looks of the characters, the bizarre wardrobes, the constantly asking "Is this character a guy or girl?"). I miss the days when Final Fantasy actually took place in FANTASY settings. I'm talking Final Fantasy 1 - 6. There were some high-tech elements within them, but for the most part your still visiting a king in Castle FillInTheBlank, your characters us swords and spears and bows and such, and an airship was literally a sea-fairing ship combined with the helocopter.
But most importantly: there were no direct sequels. Each game was a world and universe unto itself, and I guess for all the tl,dr people out there, the over all point is this: the reason direct sequels to FF games don't do well is because they feel foriegn to fans of the series. FF games aren't supposed to have sequels, they're supposed to be good enough to stand on their own merits. FF games are supposed to end on a definite note, that the evil has been vanquished and they lived happily ever after, the end.