At what age do professors stop taking new students? Assuming STEM, At what age do tenured professors stop taking new students?

I am a first year PhD student and have my eye on one professor who seems to be really interesting and I feel he finds me as a good candidate too but for some reason that he refuses to discuss he does not wish to take me in. Most of his current students are 1-2 years from graduating.

I have a strong reason to believe that it's his age (60-65). That's when I thought about the more general question I am asking.
There are no hard and fast rules for this. However, in general, the question is not so much time-after-PhD, but rather time before retirement. Most faculty advisors in the final stages of their careers stop taking students, so that they can wind their research groups down gracefully. Frequently, the last years before retirement will be spent writing and teaching, and mentoring a few additional students. The amount of time depends on the average career of a graduate student in the professor's particular discipline, but somewhere between three and seven years before retirement, the "wind down" will begin.