This is a serious question seeking sources that discuss the topic.
I speculate that a father that regrets his son being born, does not support him, does not teach him Torah or Mitzvos etc., is considered "תוהא על הראשונות" (Rambam: one that regrets doing a Mitzvah is not rewarded for it.) may somehow lose his right to Kibud Av of the child.
Maybe serious child abuse or even rape can suffice.
Any sources or thoughts on this?