"The children's needs don't go away because the job did."
That's true, but when a father has lost his income, it's understandable that he can't always pay the same amount he has been. If the marriage was still intact, the loss of income would be the same. Child support is not just for the kids. It goes to the other parent - usually the mother, and she uses it for whatever she wants.
I have seen fathers living in a $200 a month room, eating ramen noodles every night, paying ridiculous amounts of child support, while the mother drives a new car, lives in a nice big house, and has all the latest "toys". That is wrong.