One problem is that the salaries and benefits are not competitive with public schools. Around here, an experienced public school teacher makes more than $55k. The teachers in some of the less successful Catholic schools were making less than half and the quality of the faculty suffered.
A BIG part of the problem is the insistence on "certified" teachers (aka graduates of "colleges of education". My wife and I are both Catholics (her cradle, me convert last year) and PhD chemists, and are due to retire soon. We would LOVE to teach at a Catholic school, probably just for benefits (health insurance). We could certainly handle chemistry and general science, and with a little mentoring, physics and math. But neither of us is "certified" (of course, if we taught at university, we WOULD be qualfied to "teach the teachers").
I'm sure we're not the only ones out there.