In family psychology are there any normal (not abnormal) reasons to give up and cut off communication with your child (adult or otherwise)? I would think it would be rational to have a closed adoption of a baby and communication might need to stop if the child presents a constant danger.
A cuckolded father would be likely to reject a child who is discovered to not be his own. From evolutionary perspective, men who get cuckolded and take care of a genetically-distant man's child would fail to reproduce their own genes and increase the chance of survival of the genes of the other man who did the cuckolding. Thus rejecting such a child would be an evolutionary adaptation to the problem of paternity uncertainty.
Another reason could be that the mother misjudged the commitment of the father, and mated before such bond was established. This could be in combination with a father who's mating strategy favors fertilizing high quantity of women over investing in few offspring with one woman.