A former Waikato woman has admitted causing the death of her newborn baby after getting drunk and falling asleep while breastfeeding her.

The nine-week-old's death happened just six days after she was released from Waikato Hospital after another incident, in which her mother had arrived home to find her daughter smothered with a blanket and struggling to breathe.

In the Hamilton District Court yesterday the 28-year-old mother, who was granted interim name suppression by Judge Barney Thomas, admitted a charge of failing to provide the necessaries of life for her daughter by omitting to provide the child with a safe sleeping environment, therefore causing the child's death on February 19, 2012.

Judge Thomas convicted the woman - who was supported in court by her family and three-month-old baby - and remanded her for sentencing in January.

The court heard the woman arrived home drunk about 2.45am.

Walking into the bedroom she noticed a small mound under the blankets of her bed shaking.

The woman, who has four other children, pulled back the blanket to find her daughter hot, shaking and distressed.

The infant was taken to Waikato Hospital, where she stayed until February 13.

On being discharged, the woman was given a pepi-pod and information about keeping baby in a safe place to sleep.

However, on February 18 the victim, her partner and family went to a friend's housewarming party where the woman became drunk.

The baby had been put to sleep in a bed in the house, but during the early hours of the morning, the woman decided to pick her up and put her into bed with her and her partner and their two-year-old child.

The woman then began breastfeeding her daughter, but fell asleep.

They slept for a few more hours.

Later, on two separate occasions, a family member and a friend noticed the baby appeared hungry and was crying and tried unsuccessfully to wake the woman.

At one stage the blanket had completely covered the baby.

As they couldn't wake the woman, and with the baby still crying, they put the baby back on the woman's breast to continue to feed as she slept.

However, about 4.55am, a friend walked past and noticed something wrong with the baby.

The woman and her partner were woken and CPR was carried out, but the baby was unresponsive. St John Ambulance staff were also unable to resuscitate the baby.

A post mortem examination reported the death as being sudden unexpected death infancy [SUDI], associated with an unsafe sleep environment, causing accidental asphyxia.

When spoken to by police, the woman accepted her baby died as a result of her not putting her baby somewhere safe to sleep.

In his application for name suppression, the woman's lawyer James Gurnick said he accepted the printing of her name would not affect his client, however it could pose significant challenges for her four other children.

Her eldest, a son aged nine, had already been teased at his local primary school.

Police opposed the name suppression application and Judge Thomas indicated that although there were no grounds for the application, he would grant it temporarily to allow Gurnick time to file a more exhaustive application outlining the "extreme hardship" the family would face.