What did the boy mean when he said his father's eye was going away?
Well, from what text are you asking this question?
But to take a stab at answering this question without knowing the context in which it was used, I would venture to say it could mean one of two things (in my mind):
1) The father's eyesight was failing and blindness was setting in. Not just blindness in a natural sense in that he could no longer see someone's face, read something, or enjoy a sunset, but also that because of this natural blindness, he was losing a grip on the world around him and was slowly losing touch with reality and the sense of knowing how everything fit or worked together--all because of his losing his sight.
2) Or, it could also mean that perhaps the father had someone who was spying or following the boy in a "big brother" sense. No longer did the boy feel that he was being watched 24/7 and being scrutinized in everything that he said or did. And because this "eye" was going away, now the boy is free to actually be himself and mature into being his own person without having to answer to the expectations of his father.