The 76-year-old has already failed in his bid to overturn a separate conviction over the murder of his wife Lynette in January 1982.
He has been sentenced to a maximum of 24 years for the homicide.
The conviction was upheld by the NSW Court of Criminal Appeal on Friday.
Justices Kristina Stern and Sarah McNaughton – who oversaw an appeal hearing in March – ruled to dismiss Dawson’s legal challenge.
Justice Peter Hamill was the lone judge in dissent, saying he would have allowed the appeal and quashed the conviction.
The full reasons of the court have yet to be published.
The carnal knowledge sentence, which relates to a former student known as AB who later moved into his home, added one year to his non-parole period.
At an appeal hearing in March, Dawson’s lawyers attempted to cast doubt on AB’s claims she had been sexually abused before her 17th birthday.
A person can only be convicted under the carnal knowledge offence – which was in place in 1982 – if the complainant is between 16 and 17 years old.
Dawson also claimed the verdict was unreasonable, asking the NSW Court of Criminal Appeal to overturn it.
The then-PE teacher groomed AB during fitness classes and organised a tennis match so the girl could meet his wife and start babysitting, a District Court trial was told in 2023.
The teen started sleeping with Dawson and eventually moved into his home soon after Lynette was murdered and he disposed of her body, the NSW Supreme Court found when he was convicted over the killing in 2022.
Dawson is incarcerated at Sydney’s Silverwater prison.
His 18-year non-parole period for murder expires in 2040.