Child protection authorities were warned 11 times of dangers to a three-month-old Canberra girl before her death.
Family members found the infant dead in her cot in September and the cause of death remains unclear.
In the months leading to her death, ACT Care and Protection caseworkers received reports that her father was violent and her mother may have been smoking the drug ice.
Worries were also raised that a doona had covered the baby's face while she slept with her mother.
The troubled family, which cannot be identified for legal reasons, first came to Care and Protection's attention in 2010, when the young mother was pregnant with another child.
They again became a subject of concern in March this year, when officials received five reports in the second half of the month.
The concerns included parental drug use, inappropriate care arrangements and domestic violence.
The pregnant mother was offered and accepted prenatal support.
A further four reports were made between April and July, expressing concerns that the mother could not protect the children from their violent father.
In another incident, an intoxicated paternal grandmother allegedly dragged the mother from her bed over suspicions she was using drugs and neglecting her other children.
In July, the mother was counselled on the dangers of co-sleeping after she reportedly allowed a doona to almost completely cover the child's face while they were in bed together.
The report noted holes in the walls of the home and a large gash on the father's hand.
In August, the baby missed three immunisation appointments.
The next month, police attended the home after receiving a triple-0 call.
The mother denied calling them and officers saw a pipe used to smoke methylamphetamine in her purse when she retrieved her phone.
The children were with their aunt at the time, who told officers the mother had dumped them so she could go on a bender.
Care and Protection's after-hours crisis service visited the home two days later and said it was messy and untidy.
The mother left the children in the shower unsupervised while speaking to caseworkers and had to be prompted to check on them.
The baby was found dead in late September.
Police have conducted an autopsy and are preparing a report for the coroner.
The older siblings were moved into the care of relatives after the death.
The girl is one of three children known to Care and Protection to die in the ACT in the past five years.
The authorities do not publish statistics on the cases for fear of identifying the children or their relatives.
The ACT government is the guardian of about 550 children and keeps tabs on more than 1000 minors.
Care and Protection Services received 14,972 child concern and child protection reports in 2012-13, up from 12,419 in the previous year.
A Community Services Directorate spokesman said not all reports required a statutory response; in some cases, early intervention programs supported families where no risk to children had been identified.
"Care and Protection services' core responsibility is to assess children who are at risk within their family and respond to their needs within a statutory framework," the spokesman said.
"Children and young people who are the subject of multiple concern reports and/or child protection reports need to be identified for further consideration.
"This would allow early intervention assistance to be provided."
An ACT Auditor-General's report, published in March, found the directorate needed a better system of monitoring children who needed further consideration after being reported.