The 52-year-old man, who can't be named, was previously acquitted at separate trials of murdering two of the children - four-year-old Evelyn Greenup and Clinton Speedy-Duroux, 16 - in late 1990 and early 1991.

The NSW government applied to the Court of Criminal Appeal to have the acquittals overturned and a retrial ordered to include a charge of murdering a third child, Colleen Walker, 16, who disappeared around the same time.

It argued that there was fresh and compelling evidence - relating to Colleen's disappearance - to justify the overturning of the acquittals and a retrial.

Under NSW double-jeopardy laws revised in 2006, a person can be tried for the same crime for which they have already been acquitted provided there's fresh and compelling evidence.

But the court dismissed the application on Thursday, finding there was no fresh evidence in Evelyn's case and Clinton's case could not be considered by itself.

Relatives of the three children said they were "devastated but not down" by the decision and, despite having been "kicked in the guts by the court system and the law" would continue fighting.

Attorney-General Mark Speakman later said he would seek legal advice about the prospects of applying for leave to refer the case to the High Court.

"Today may not be the end of what has been a hard, devastating, distressing road for the Bowraville families and I'll be urgently considering what remedies are available either legislatively or in court in the coming days," he told reporters.

Australian Associated Press