Receiving recommendation letters after graduation
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.