Kathleen Folbigg has failed in a bid to overturn a finding of her "certain" guilt of killing her four children, despite having some science on her side.
The NSW Court of Appeal on Wednesday dismissed Folbigg's judicial review application, upholding the results of a 2019 inquiry by former NSW District Court chief judge Reginald Blanch QC.
He found significant investigations had failed to find a reasonable natural explanation for any of the deaths of Caleb, Patrick, Sarah and Laura, who all died before their second birthday in the decade to 1999.
Folbigg's own explanations and behaviour in respect of her diaries, which weren't available in any of the mother's criminal appeals, made "her guilt of these offences even more certain", Mr Blanch concluded.
The appeal court found there was "ample basis" for Mr Blanch's conclusion.
"This was not a case in which the judicial officer's conclusion was at odds with the scientific evidence," the court said.
"The scientific evidence raised a theoretical possibility that there were innocent explanations for the deaths of the two girls."
That theory focused on changing levels of amino acids in the body, including that the change was hereditary.
Scores of scientists have called for Folbigg to be pardoned by the NSW governor, claiming the latest court process didn't examine new scientific evidence available since Mr Blanch's inquiry.
Her supporters say Sarah, Laura and their mother share a genetic mutation that has been linked to sudden deaths in young children - a theory Mr Blanch concluded didn't raise reasonable doubt.
The appeal court agreed.
"When these matters were weighed with the inculpatory inferences derived from Ms Folbigg's diary entries and her evidence in seeking to present innocent explanations of them, there was an ample basis, consistent with the scientific evidence, for the judicial officer to conclude that there was no reasonable doubt as to Ms Folbigg's guilt," the court said.
Folbigg was ordered to pay the state's legal costs for February's two-day hearing.
She is serving a 25-year minimum term, having lost three appeals against her 2003 convictions, including one in the High Court in 2005.
The petition currently before NSW Governor and former senior judge Margaret Beazley deals with matters not considered by the appeal court, its authors said.
"The decision of the Court of Appeal does not end the legal avenues available to Ms Folbigg," barrister Robert Cavanagh and solicitor Rhanee Rego said.
Australian Academy of Science president John Shine said it was "deeply concerning" there was no mechanism to appropriately weigh up all medical and scientific evidence in a case such as Folbigg's.
"Expert advice should always be heard and listened to. It will always trump presumption," another signatory, former chief scientist Professor Ian Chubb, said in a statement.