Are professors more likely to ignore students who are no longer
affiliated with the school?
They often show the tendency for presenting the recommendation for the students, who had a live impact in their minds in view of academic performance, personality and so on. You can't expect from a professor to write anything useful about you, when he/she even can't recall you, deservedly.
On the other hand, leaving the academia and the school, within which the professor is affiliated, would not lead to his/her certain ignorance. In my own explicit experience, one my professors did present an awesome LoR for me, even though I'd left the department for more than 3 years. He did that with due attention to our constant communication and collaborating on some research stuffs.
is it fine to accept recommendation letters from professors who taught
courses that I received my minor in?
Yes. The recommendation should come from the person, who can depict you, as well as possible. The lecturer of a minor course, could who be able to hit this mark, would be a right choice.