I have said this about a bazillion times here but it bears repeating: Private schools, and faith based schools in particular, are going through a Darwinian process. That is to say that if they don't adapt/evolve quickly enough to changing circumstances, if they are more reactive than proactive, if they don't spend money to make money in terms of fundraising and achieving a strong financial footing, then they will not survive. Period.
I have also said quite frequently that private schools that wind up closing typically endure death by a thousand cuts. Those cuts are the equivalent of enrollment decreases that, when you look at them on an annual basis, seem relatively painless. Because they are relatively painless, the schools take relatively painless measures to try to stop or reverse the decreases. To continue the bleeding metaphor, they use a tourniquet or a bigger bandaid to treat the cut but they don't treat the underlying causes of the bleeding. They wait too long to amputate a limb or to try a drastic and promising new treatment. The years turn into decades and, before you know it, what they knew at the time was unsustainable in terms of enrollment declines in the long term results in nothing left to sustain.
The above is speaking in general terms. While the gist of it applies to most, it does not apply to all. There are examples, right here in our state, of private schools that have either successfully reinvented themselves or have simply started brand new with an attractive and affordable educational model. The Cristo Rey schools (Cristo Rey Jesuit, Christ the King Jesuit, and Cristo Rey St. Martin) come to mind as good examples of successful startup high schools. San Miguel School and Chicago Jesuit Academy are good examples of successful middle school startups. DePaul Prep is a good example of reinvention driven by great leadership.
The key to the above is leadership. Not just good leadership, but great leadership that sets high expectations and motivates the school community to exceed them. In order to thrive, a private school needs great volunteer leadership in the form of a governing board that knows its mission is to advance and enhance the school's mission. It needs board members who know they need to give, to get, or to git! It needs great academic leadership that is consistent, effective, proactive, and responsive to the needs of the greater school community.
The problem with many private schools and Catholic schools in particular is that they operate on a shoestring budget and have done so for decades. They can't figure out how to climb out of that space between a rock and hard place. So, they make do. They cut corners. They squeeze themselves in between a bigger rock and a harder place, creating a tighter space from which it becomes increasingly difficult to find a way out. And, in doing that, they get what they pay for. They get ineffective marketing efforts that produce enrollment declines. They get lackluster fundraising efforts that don't maximize the giving potential of their constituents. They get a revolving door of mediocre academic leaders. Mediocrity begets mediocrity.
Sure, all those things (rising tuition, smaller Catholic families, etc.) that others have mentioned in this thread are factors. But, the fact that some schools are super fit and healthy while many are in an early, middle, or late stage of bleeding out makes me think that those other factors are not as important as the leadership factor. Great leadership is the common element that you will find in those successful schools.
Have a nice day.