Robinson was 35 and had five children of her own when she fatally assaulted Melissa in January 2009. Melissa and her older sister had gone to live with Robinson and her husband, Brent, on a dairy farm in November 2005 - the final two of 18 children the couple had fostered in three years.
Melissa died in hospital when her life support was turned off on January 8, 2009, four days after being rushed by ambulance to Tauranga Hospital and then on to Starship Hospital in Auckland for surgery to remove a clot on her brain.
The trial was told Melissa died from severe subdural bleeding, a traumatic brain injury, caused by being shaken.
But Robinson initially told emergency services on the phone that the injury occurred when Melissa fell over and banged her head. She later told the attending St John Ambulance officer she had fallen from the portacot she slept in during the day.
However, medical experts testified that her injuries were not consistent with such a fall, and said Robinson had told a social worker and a police officer she had shaken the child.
The baby's injuries included bruised earlobes, a bruised forehead, bleeding behind an eye and abrasions on her cheek.
Justice Tony Randerson said in the Court of Appeal decision, released today, that Justice Stevens had considered a psychiatric report at sentencing which showed Robinson had suffered "significant personality dysfunction and adjustment problems subsequent to the victim's death".
"Amongst other things, she was admitted to psychiatric hospitals on three occasions and suffered a motorcycle accident in 2006 which resulted in the amputation of her left leg below the knee.
"The judge recognised that the appellant would require support from the Regional Forensic Psychiatric Service while in prison."
However, Justice Stevens had to consider up those factors against the level of violence involved in Melissa's death, the distress to the baby's family, the abuse of a position of trust given Melissa's young age and the fact she had been placed with Robinson for safekeeping.
"The judge did not consider there were any mitigating factors relating to the offending but took into account the appellant's previous good record and reputation in the community, some limited remorse and the mental health issues which she had suffered since the death of the child. He noted that the appellant continued to deny the offending."
But Justice Randerson said in his decision Justice Stevens should have allowed a greater discount for Robinson's mental health, disability and remorse than the combined 12 months that he did.
"(A psychiatrist's) report confirms that the appellant's mental state prior to the offending was stable and she was a fully functioning member of the community, raising her children, working on the farm and undertaking voluntary work. In marked contrast, her mental state deteriorated seriously after the child's death," Justice Randerson said.
"By any measure, the stress she suffered was severe, requiring several admissions to psychiatric hospitals and resulting in the loss of her leg in an accident which (the psychiatrist) considered was related to the psychiatric problems she was experiencing at the time.
"Her distressed state of mind is further evidenced by her contrasting responses to the child's death, ranging from anger towards those she considered to be at fault to heart-felt expressions of love for the child and regret over her death."
The Appeal Court also considered her suffering in the nearly four years between Melissa's death and Robinson's sentencing "warranted a significantly greater discount than the judge allowed".
"The level and length of her distress to date is substantially more severe than is commonly encountered in similar situations," Justice Randerson said.
The additional difficulties Robinson would face in prison as a result of her amputation were not "disproportionately severe" but the fact the loss of the limb occurred as a result of her high levels of stress and anxiety after Melissa's death should have been considered in assessing the appropriate sentence.
Robinson had abandoned her appeal against conviction, which showed she had accepted the jury's verdict, he said.
"That is an important factor since it demonstrates she has accepted responsibility for her offending.
"We consider the appropriate discount for all relevant factors is two years overall. That would result in a final sentence of five years and six months imprisonment."