A homicide investigation into the deaths of a two-month-old girl and her six-week-old brother appears to have stalled.

The deaths of two infant siblings 14 months apart are suspicious, police have confirmed.

However, a lengthy homicide investigation appears to have stalled and the coroner will likely be left to determine what happened to the two-month-old girl and her six-week-old brother.

The children both lived at a property their parents rented in Canterbury.

The girl died in May, 2015. Her brother died in March, 2014.

READ MORE: Police investigate 'unexplained' deaths of a woman's two babies in Canterbury

Stuff has chosen not to name those involved because of the extremely sensitive nature of the case.

Police previously said the circumstances of the deaths were similar.

In both cases, the children's mother, aged in her 20s, told investigators she put them to bed in the morning after they were fed. A short time later she went to check on them and found they had stopped breathing. The woman's partner was not home at the time.

In September 2015, police said the children's deaths were unexplained.

This week, Detective Inspector Greg Murton confirmed they were being treated as suspicious.

"We investigated because there were concerns about the circumstances surrounding both deaths. That has not changed," Murton said.

"Considerable resource" had been dedicated to finding out what happened to the children. Several experts were consulted on a "range of issues", he said.

The investigation spanned two to three years. The mother and her partner were both formally interviewed by police as part of the inquiry.

The last "active inquiries" were made by police about a year ago. The file had since been reviewed, Murton said.

"The deaths were fully investigated at the time and all available evidence ... was obtained.

"If any new information comes to hand that will be followed up on."

Murton said that while he would like to comment further about the deaths he was unable to do so.

"It's for the coroner to ... determine causation."

Police previously said both the children were healthy in the hours before they stopped breathing.

Investigators looked at the possibility the deaths were the result of factitious disorder in another, also known as Munchausen syndrome by proxy, a form of child abuse where a person harms someone to garner sympathy from others.

Tests were done to see if there were any genetic factors at play.

The mother posts regularly on Facebook about the pain of losing her children and is a member of several groups dedicated to sudden unexplained death in infancy (SUDI).

In August, the woman said: "I would … trade my life so I could have one more cuddle with them."

She did not respond to requests for comment.

What is Munchausen syndrome by proxy?

Munchausen syndrome by proxy is a rare disorder that involves a parent inducing an illness in a child they are caring for, often to attract attention.

Auckland psychologist Rebecca Daly-Peoples said people suffering from the syndrome were difficult to identify because they often presented as perfectly functional people.

"It's a cry for help. Rather than someone harming themselves, they harm their children and then they take them to hospital.

"Fundamentally it's a psychological disorder and the individual is needing psychological assistance."

It appeared cases rarely ended in death, Daly-People said.

"It's more frequent hospitalisations and reports of injury."

In 2013, a court heard how Auckland mother Shayna-Lee Broadbent, 20, who repeatedly suffocated then saved her newborn baby and then cried out for help, probably had the condition.

Broadbent pleaded guilty to causing grievous bodily harm with reckless disregard and was sentenced in the High Court at Auckland to 11 months home detention.

WHERE TO GET HELP:

1737, Need to talk? Free call or text 1737 any time for support from a trained counsellor

Lifeline – 0800 543 354 or (09) 5222 999 within Auckland

Youthline – 0800 376 633, free text 234 or email talk@youthline.co.nz or online chat

Rural Support Trust Free call 0800 787 254

Samaritans – 0800 726 666

Suicide Crisis Helpline – 0508 828 865 (0508 TAUTOKO)

What's Up – 0800 942 8787 (for 5–18 year olds). Phone counselling is available Monday to Friday, midday–11pm and weekends, 3pm–11pm. Online chat is available 7pm–10pm daily.

Kidsline – 0800 54 37 54 (0800 kidsline) for young people up to 18 years of age. Open 24/7.

thelowdown.co.nz – or email team@thelowdown.co.nz or free text 5626

Anxiety New Zealand - 0800 ANXIETY (0800 269 4389)

Supporting Families in Mental Illness - 0800 732 825.

Alcoholics Anonymous - 0800 AA WORKS, or aa.org.nz.

Alcohol Drug Helpline - 0800 787 797

Alcohol Anonymous family group - 0508 425 2666