Now I may not be speaking for everyone, but for me, XIII's major problem was an inappropriate ratio of story, combat, and plot relevant combat. Now that probably sounds a little strange since most people only mention the first two, but here's why I think other games did things in a pretty okay way while XIII should have rethought most of its gameplay and traveling sections.
XIII has a very high level of plot immediacy. The game plays certain parts almost as if in real time. In such a scenario, there is nothing more disheartening than seeing a corridor that is absolutely jammed to the brim with enemies that have no bearing on the story. In X or XII there were a lot of creatures on the way, but in those games a lot of room was left open where traveling WAS the plot point, so it made perfect sense to drop enemies on the way. That puts a challenge on the road to the next major plot point without deterring from it. XIII had so much of this that novel seeming combat fell into tedium and the story wasn't kept tight enough to provide the level of interest and depth that I and I believe many other fans desired from the game.
So XIII missed the point, and it seems like XIV's launch has been an unmitigated disaster. Worse yet, Square has decided to make a spin-off of XIII as if they were completely out of touch with a large portion of their North American and British fanbase (I can't speak for the Japanese) or as if they gave the project the go-ahead before XIII was even on shelves. Does this spell the end for the series? I don't think so, I just think it marks a very pathetic resolution to this anniversary celebration of having 6 titles in a compilation for Final Fantasy XIII. Terrible execution, but they're not going to tank the core franchise that makes up both companies these days because of this venture. They've still got plenty of capital. Now if XV also fails, then you can pretty much call this series dead in the western market.
EDIT: http://www.gametrailers.com/game/the-final-fantasy-retrospective/4831
Watching that again, the series really has fallen from grace quite badly since XII's release (that doesn't include XII, I loved that game). If Versus doesn't turn out to be great or the next numbered title in the series doesn't add up to our expectations, the market for this game will shrink by quite a bit.