In a recent episode, the baby's father Chris Warner suggested the mother abort the pregnancy after learning it might have Down syndrome.
That's angered the Down Syndrome Association who say they weren't consulted about the episode.
Down Syndrome Association spokesperson Kim Porthouse told Morning Report the storyline reflected outdated thinking and failed to represent an inclusive society.
"People who are either going through this process right now, people with Down syndrome who watched the programme, parents of children with Down syndrome are finding this aggressive forceful reaction quite inappropriate and offensive," she said.
South Pacific Pictures produces the show for TVNZ.
In a joint statement, it said it had considered the association's feedback and were aware the storyline was a sensitive topic.
It said producers worked with medical advisors to ensure health matters were depicted with care.