Karl, the youngest of seven children, died while in the care of Ngatai-Check on October 24, 2009.
He had been asleep on a couch and had woken with wet pants.
Ngatai-Check, who had been spotting cannabis, spun the toddler around and he hit a coffee table, breaking ribs that punctured his right lung and caused bleeding in his chest cavity.
The child was then left in a toilet for five or 10 minutes while Ngatai-Check left to play video games in a bedroom.
When Karl came into the room, Ngatai-Check kicked him in the stomach, causing internal tissue to tear and then he kicked him harder.
The little boy was rushed to Wanganui Hospital with fatal injuries.
A Supreme Court decision released today said Ngatai-Check sought leave to appeal against his conviction.
The issue related to evidence by paediatric surgeon Professor Kevin Pringle, who described the fatal kick as being delivered "with venom".
Ngatia-Check argued the Court of Appeal failed to put sufficient weight to the "highly prejudicial effect" of the evidence, the decision said.
He also said that he did not file papers to seek leave to appeal against the Appeal Court's decision, because when it was delivered he was so distraught and "shell shocked" he gave up hope of another appeal.
The Supreme Court decision agreed with the Court of Appeal that there was no risk of a miscarriage of justice.
It granted an extension of time to make the application for leave to appeal, but that application was dismissed.
