In 2007 they moved to Australia, and in 2009 police asked them to return to New Zealand to discuss the allegations, but the pair refused.
"This refusal, combined with limited police resources, resulted in the investigation being put on hold," the ruling said.
In 2014 the Anguses moved back to New Zealand and came to police attention, allowing the investigation to start back up.
In early 2016, police charged them jointly with 10 counts of theft by a person required to account and three counts of theft by a person in a special relationship.
By the time police were able to charge them, five of the complainants had already died.
The current appeal was advanced by Melissa Angus, who initially pleaded not guilty and elected trial by jury.
She applied for a stay of prosecution, arguing her right to a trial without undue delay had been breached, but the District Court declined it.
She then chose to switch to a judge-alone trial, and a week before the trial was due to start she pleaded guilty following a sentencing indication.
Angus received a sentence of six months' home detention and was ordered to pay $10,000 in reparation at $100 per week.
She has since argued the court was wrong to decline her application for a stay of prosecution, and wishes to appeal her convictions - but filed her appeal too late, and in the wrong court.
In declining the stay application, the District Court judge said while the delay in bringing the matter to trial was undue, it was not egregious and there had been no prosecutorial misconduct.
The Crown case was considered strong, relying on "an abundance of documentation".
Angus has applied to the Court of Appeal for an extension to the time for filing appeal, as her appeal was filed about two months out of time.
But due to a jurisdictional issue brought about by a legislative change to procedure affecting appeals filed after November 2018 the Court of Appeal declined the application for extension to filing time, because it was filed in the wrong court.
According to a liquidator's report, the business went under following a "severe downturn" in business, the result of "negative publicity" around a dispute over a funeral that had been carried out.