During the incident in January 2015, Simpkins and his father chased three boys after one stole a pair of shoes from outside their house.
Once caught, Simpkins pinned one boy on the ground and punched him in the head more than once.
He also kicked or punched the boy in the stomach, winding him, and later punched one of the boys in the face, knocking him to the ground.
Two boys were taken to hospital where they were treated for injuries. A third boy was uninjured but shaken.
In the appeal, Simpkins' lawyer submitted the offending was not "deliberate and gratuitous", the judge placed too much weight on what she considered the unlawful detention of the boys, the judge failed to give sufficient weight to the fact that the complainants had committed a "burglary", and the judge erred in describing the behaviour as "vigilante".
But these arguments were not accepted by the Court of Appeal.
The judgment stated the critical issue was the new evidence, being the confirmation from Rotorua Boys' High School board of trustees deputy chairman Mark Lawrence that in the absence of a discharge, Simpkins could not continue his employment at the school because of provisions in the Vulnerable Children Act 2014.
Mr Lawrence said the board and the school wished to retain Simpkins because he had been "hugely successful", played a "major role in the development of young people" at the school and had done "fantastic work".
"The 14 references and affidavits presented to the judge, accurately described
by her as 'glowing', make it abundantly clear that Mr Simpkins and his father are
held in high regard, that Mr Simpkins has devoted much time to developing young
men in his community and engendering in them a sense of pride, that Mr Simpkins is turning out 'many fine young men' in Rotorua, that young people respond well to
him, and that he has potential as a leader in the Maori community.
"We accept from all of this evidence that Mr Simpkins is very talented in
developing young men and that Mr Simpkins will lose his present position if the
convictions for assault on a child remain and he is not granted an exemption.
"In that respect the position is changed from that before the judge. Despite that, however, we are not satisfied that the consequences of a conviction on these offences are out of all proportion to the gravity of the offending.
"Even if aberrant and wholly out of character, Mr Simpkins' actions were an excessive, indiscriminate response to modest provocation by an adolescent, with adverse consequences for the youngest of the three complainants."
In response to the Rotorua Daily Post's questions, Rotorua Boys' High School principal Chris Grinter said it had been mutually agreed that if Simpkins' conviction was not overturned, he would resign.
"Mr Simpkins stood down from his position as director of rugby at the time of his conviction as previously advised. It was mutually agreed that if his conviction was not overturned on appeal that he would formally resign his position. This has happened."
When asked if Simpkins had been working in any capacity at the school since his conviction, a school spokeswoman said she would not comment further.
Mr Grinter said the school was "certainly disappointed to lose the services of a talented staff member and mentor for our boys".
