What damaged reputation?
You'll have to forgive me for not backing up my statements with a single statistic here mate. My opinions are based only on what I've seen and heard, both online and from friends.
I am by no means a jaded gamer. I play with an open mind and can be easy to impress. However, I don't think any of the games since X will be considered classics in years to come. In fact, XII and XIII are now 10 and 7 years old respectively and don't have the same reputation as earlier titles did after the same amount of time had passed. XII has gained a few more fans in recent years, but it's hardly a classic. And whilst commercially successful I don't think there's any great love for XIII among fans, which makes it's spinoffs a little confusing.
I think it's fair to say the recent games have enjoyed increased sales as a result of coming under the famous Final Fantasy banner. Essentially though, they're pretty forgettable. Made by someone else they would go unnoticed. People have been buying them because of the series past, only to be promptly let down. I don't think that process can go on or the sales figures will start to decline majorly. There's a generation who can see a difference in quality between the illustrious past and present. And perhaps more worryingly for the series, there's a younger generation who only know of the current games, which are hardly revolutionary like their predecessors were. There are certain series that demand your attention, releases that get everyone talking. Final Fantasy is part of that group, but is hanging on by it's fingertips.
That's why I think a lot hinges on this game. The prolonged hype will only intensify in the coming months. Older fans are interested to see if it can recapture the magic. Whilst for newcomers it could potentially be their gateway into the series.
Personally I'm wary of the changes this new game has gone through, but ultimately I'm excited about it. From what we've seen it seems to combine the elements we all love about Final Fantasy with some quirky new ideas. I've got high hopes.