The Catholic Church is an ancient institution with a rich history and culture, which in my opinion is its main appeal. But will all that history save the Catholic Church? That is to say, will all that history do the church any good in fighting off corruptive forces from within, or increased and unprecedented pressures from the world outside? It's hard to say. On the one hand, reformers need only appeal to the many examples in history of the church of mavericks who succeeded in changing it, as well as the ones who failed and were instead branded heretics and shunned. This would serve as a very good guide to what works and what doesn't work in pressuring the church to change. On the other hand, all that history so well-documented serves as a millstone around the Church's neck, providing ample reasons for leaders to drag their feet against change.
The fact is, at least in the US where I live, the Catholic Church is not doing a very good job providing for modern day people's spiritual or communal needs. And as such, it's second-rate religion. I went to several Catholic masses recently for family functions (most recently a baptism), and found it one of the most tepid and boring experiences imaginable. All the vibrancy and sense of connection to something greater was gone. The priest had no passion at all, and preached a dense, abstract, arcane, pretentiously deep sermon at (not to) a roomful of mostly poor, recent immigrants with a poor command of either English or theology. They all sat there glazed and overtired, making feeble attempts to keep their kids from talking and climbing the pews, simply because they'd been raised Catholic and still felt compelled to go.
But many people are now finding their fire better lit elsewhere, by religious (and secular) institutions that meet people where they're at, right here right now. There are groups and ideologies that are doing a far better job relating ancient stories and timeless words of wisdom with real world problems that are on people's minds today.
For one thing, I don't think most modern day Westerners relate to the archaic way the Catholic Church handles authority and decision making. Ideally, if you're going to belong to a religious group, the most fitting one is one whose political structure and chain of command mirror those of the secular institutions to which its faithful belong. Why? Because this is what will make the faithful feel most familiar and at home. A fire and brimstone preacher will reach people who were raised in houses where backtalking got you beaten, and who work for bosses who don't pay workers to think and tolerate no deviation. A circle of cushions around a sacred fire with a talking stick will appeal to people raised in houses where children were encouraged to speak freely and be spontaneous, and to people who work in companies where there's no dress code and decisions are made by consensus. But the Catholic Church is just alien in this regard. Parallels could certainly be drawn to the power structure of European feudalism and nobility. Also, I think the Catholic Church's robust popularity in pre-1960s America could very well have come from its institutional similarities to big industry, for which most Catholic Americans worked at that time. But nowadays, I think the Church's intrigues and internal machinations strike most Catholics as an anachronism.
I do think the Catholic Church has a future, just because it's so large and has such a lengthy history that enough people care about preserving. But it will probably smolder on as a much smaller institution, by orders of magnitude. It wouldn't surprise me if the church declined down to a couple million loyal and fervent keepers of the fire for a few centuries, before either experiencing a revival or burning out entirely.