Mrs Beaumont passed away on Monday in a nursing home and her death was confirmed in a notice published on Thursday.

The disappearance of her three children - Jane, 9, Arnna, 7, and Grant, 4 - on Australia Day in 1966 is one of the country's most enduring mysteries.

But despite its notoriety, Mrs Beaumont and the siblings' father, Jim, retreated from the public eye and have not spoken to the media in decades.

Their children never returned after leaving the family home for an afternoon at Glenelg Beach, sparking a widescale search operation that remains open today.

In 2013, investigators scoured a factory west of Adelaide after two brothers told police they had spent the 1966 Australia Day weekend digging a large hole on the site at the request of the owner Harry Phipps.

Phipps died in 2014 but his son, who accused his father of sexual abuse, believed he was linked to the missing children.

The factory site was excavated by police in early 2018 but only animal bones were found.

The officer in charge of Major Crime, Detective Superintendent Des Bray, said police were still investigating Phipps and remain committed to solving the mystery.

"We will always do anything humanly possible to locate the Beaumont children and take them home to their family," he said after the search wound up.

"I don't think there's anybody in the country who doesn't want to find the Beaumont children."

A police statement released after Mrs Beaumont's death noted her passing "with sadness".

"Consistent with family wishes, SAPOL have no comment to make about her passing beyond expressing our sympathy," it read.

The disappearance of the Beaumont children has been one of Australia's most prominent cold cases and subject to wild speculation at times, including possible sightings of the trio living as adults overseas.

Dutch clairvoyant Gerard Croiset was invited to Australia shortly after they disappeared, and claimed to have had a compelling vision that the children had been buried less than two kilometres from where they went missing.

Mr Croiset believed the children were buried under a brick kiln in a nearby warehouse, but extensive excavation of the areas he pointed to found nothing.

Others theorised the siblings were living in the Mud Islands, and a Perth woman came forward to claim that for about nine months in 1966 she had lived next door to the Beaumont children in an isolated railway town near the SA-WA border.

A renewed call for information on the 50th anniversary of the children's disappearance prompted hundreds of phone calls to Crime Stoppers - but all amounted to nothing.

Mr Beaumont is also aged in his 90s and living in Adelaide, but the couple separated years ago.

Mrs Beaumont's death notice said she would be privately cremated.

Australian Associated Press