The convicted killer will next week front court in Hobart for what is likely to be the final time, with her last-ditch appeal against her sentence set to draw to a close.

When Neill-Fraser’s 65-year-old husband Bob Chappell disappeared on Australia Day, 2009, an enduring murder mystery was born.

The vanishing of Mr Chappell occurred off Marieville Esplanade, in the affluent Hobart suburb of Sandy Bay, populated by stately homes and feats of modern architecture.

Mr Chappell and his wife were members of the upper crust: he a physicist at the Royal Hobart Hospital and she the former operator of a horse-riding school.

Theirs was a family marked by hyphenated last names and considerable means.

Mr Chappell and Neill-Fraser lived in West Hobart, on a leafy street lined with Federation homes.

So when Neill-Fraser, now 63, was charged with killing her husband, the case became Tasmania’s own version of Melbourne’s infamous “Society Murders”.

But unlike the killing of Margaret Mary Wales-King and Paul Aloysius King, the case of Mr Chappell’s murder is less clear-cut.

In December 2008, the deceased and his wife brought a 53-foot ketch they’d purchased in Queensland back to Tasmania, where they moored it at Sandy Bay.

The Four Winds quickly became a nuisance to the couple, requiring expensive repairs.

Witnesses at the 2010 murder trial said Neill-Fraser had, in the lead-up to Mr Chappell’s disappearance, told them her relationship with him was coming to an end.

In the most explosive moment of the trial, a witness and erstwhile friend of Neill-Fraser, Philip Triffett, told the court the accused had informed him of her plan to kill her brother in the mid-1990s.

She was said to have proposed to kill him on a yacht that she owned at the time, to weigh him down with heavy objects, throw the body into deep water and scuttle the boat.

Mr Triffett claimed Neill-Fraser had later mentioned a desire to apply that same plan to her husband.

The prosecution argued that Neill-Fraser had desired Mr Chappell’s share of the Four Winds, while Justice Alan Blow suggested she was aware that she stood to make significant material gain in the event of her husband’s death.

In the days and months following Mr Chappell’s murder, Neill-Fraser changed her story on a number of occasions when talking to the police.

After a jury found her guilty of murdering her husband in 2010, Neill-Fraser was convicted on circumstantial evidence alone.

In passing sentence, Justice Blow observed that Neill-Fraser had led a “blameless” life.

“Otherwise, there is almost nothing that counts in her favour for sentencing purposes,” he said.

“She did not plead guilty. She has shown no remorse. She has not said or done anything that would assist in the finding of the body.

“There is no suggestion that Mr Chappell said or did anything to provoke this crime.

“It was a deliberate killing for the purpose of some sort of personal gain.”

Justice Blow jailed Neill-Fraser for 26 years, with a non-parole period of 18 years.

Nonetheless, there was no smoking gun in the case of Mr Chappell’s disappearance, which has given an odd sense of hope to Neill-Fraser’s supporters - of which there are many - in the years since she was jailed.

It is principally on this ground that her lawyers have appealed against her sentence over the past eight years.

The detection of a 15-year-old street kid’s DNA on the Four Winds has confounded followers of the Neill-Fraser saga, and has informed her defence’s case for a fresh trial.

It’s nigh on impossible to determine whether or not the teen girl’s DNA came to be on the Four Winds through primary or secondary transfer - it’s been speculated it could have found its way on the yacht via a police officer’s shoe.

The girl herself denies ever being on the Four Winds on January 26, 2009.

Neill-Fraser has appealed against her sentence for the murder in both the Court of Criminal Appeal and the High Court.

In 2012, Tasmania’s former Chief Justice Ewan Crawford ruled that her original sentence was “more severe than I would have expected” and so reduced it to 23 years’ imprisonment, with a non-parole period of 13 years.

However, he dismissed Neill-Fraser’s bid to have her conviction overturned.

“She killed Mr Chappell by using some form of violence, possibly by striking him from behind with a heavy object, implementing a plan she concocted in the mid-1990s,” Chief Justice Crawford said.

Neill-Fraser then took her case to Canberra, to be assessed by the High Court. She was unsuccessful.

Her barrister Michael Croucher raised the issue of the girl’s DNA.

“[The girl] does not dispute that she is in the vicinity generally of the town, of Hobart, on the night, and subsequent material shows that in fact she was supposed to be going to a place called Mount Nelson which is just near Sandy Bay,” he said.

“Defence counsel and therefore the applicant were shut out from developing this.”

The Coroners Court investigated the death of Mr Chappell in 2014, deciding against holding an inquest.

Coroner Glenn Hay was not convinced there was “cogent” evidence to suggest Mr Chappell died in any other way than was landed on in the trial.

Neill-Fraser has now exhausted all avenues of appeal by launching a last-ditch bid to force a new trial.

The ageing inmate is the first person to launch an appeal under state legislation allowing the Court of Criminal Appeal to hear a second or subsequent appeal from a convicted individual.

Neill-Fraser’s final appeal, which is being heard by Justice Michael Brett, began in Hobart in November last year.

After several hearings, the appeal was adjourned until August 21.

The first week of the appeal featured a colourful cast of characters, including a man claiming to be an ASIO operative and a Sandy Bay resident who, in true Hitchcockian fashion, uses a telescope to observe passersby from his home near Marieville Esplanade.

Next week, the defence is set to call a key witness who will expound on the science of winching, in the hope it will convince the court that Neill-Fraser may not have had the strength to manoeuvre Mr Chappell into the water.

Either way, Neill-Fraser’s ultimate fate will be known soon enough.

But will speculation and amateur sleuthing be tempered as a result? Not likely.