Former Sydney teacher Chris Dawson has lost an appeal over his conviction for murdering his first wife, Lynette Simms, more than four decades ago.

Dawson is serving a maximum 24-year jail sentence, handed to him by a NSW Supreme Court judge who acknowledged that the lengthy term and his ailing health will likely mean he will die behind bars.

Lynette Simms vanished in 1982 and her body has never been found.

During an appeal last month, Dawson's lawyer revisited the suggestion Ms Simms may have instead left her family, while also arguing Dawson suffered forensic disadvantage in defending himself so long after the disappearance.

The Court of Criminal Appeal has today dismissed the appeal, with all three judges who sat on the appeal panel in agreement.

Dawson's appeal was based on five grounds, including that the trial judge made a legal error by not sufficiently taking into account the forensic disadvantage suffered in defending the charge so long after the disappearance.

His lawyer, Senior Public Defender Belinda Rigg SC, also took the court to evidence about Dawson's relationship with Ms Simms, as a way to revisit the alternative theory for Ms Simms going missing — that she may have chosen to leave her family.

She suggested the evidence showed a level of despair in the months leading up to her disappearance and said Ms Simms was well aware of Dawson's capacity to care for their children.

But the Crown rebutted this, highlighting the weight of evidence that suggested it was "inherently unlikely" a woman who adored her husband and idolised her children would make such a choice.

Ms Rigg pointed to a long-distance phone call Dawson said he received from his wife, during which he claimed he was told she needed time away.

The court was told Dawson had lost the ability for that account to be verified by phone records.

Justice Ian Harrison, the trial judge, found that the phone call was among a series of lies told by Dawson.

Brett Hatfield SC, for the Crown, told the appeal hearing there was no significant possibility an innocent person had been convicted in the case.

He argued that there was no reasonable hypothesis consistent with innocence.

Mr Hatfield said Dawson's account of the disappearance should be disregarded because according to him, Ms Simms never spoke to anyone after she went missing except him on the phone.

He characterised a so-called "affair" with a woman only known as JC as being marked by "desperation and obsession" from Dawson.