During the young woman's 24-hour ordeal, Lihou violated her repeatedly and frog-marched her across 9km of open country.
She was rescued after a farmer came across Lihou and the woman in a hay barn and called the police.
In 2015, Lihou tried to get the Court of Appeal to overturn his convictions and preventive detention sentence for that offending but was unsuccessful.
Since then, Lihou, a ward of the state from the age of 10, has made a submission to the Royal Commission of Inquiry into Abuse in State Care and has received a settlement from the Crown for the ill-treatment he suffered as a child.
The details of the settlement have not been made public.
In January this year, he presented his royal commission submission and recent psychological assessments to the Court of Appeal, asking it to allow him time to appeal against his sentence again.
The Court of Appeal bench of three judges dismissed his request, even though it accepted the royal commission submission was fresh evidence.
"The recent psychological assessments and the applicant's submission to the royal commission outline the tragic events of the applicant's childhood and teenage years and the effects that has on his mental wellbeing," said the Court of Appeal decision, issued on Friday.
"It is clear that the applicant's treatment in his childhood and youth was extremely traumatic and that this has affected him profoundly," it said.
Despite this, the judges said that Lihou had not co-operated with a consultant psychiatrist and a clinical psychologist who were asked to prepare reports for the sentencing judge in 2013.
They also said the previous appeal court decision had found the case for preventive detention was "clear-cut".
"We do not consider there is any indication of a miscarriage of justice in the way the Court of Appeal assessed the appeal against sentence," the judges said.
"Whatever weight is given to the applicant's personal circumstances, this could not outweigh … the high risk that he would commit further serious offences."
Lihou's abduction of the woman in 2012 was similar to an earlier crime, in 1988, when he marched an ill-clad 16-year-old girl across North Canterbury for several days, sheltering in huts, empty houses and under trees.
He raped her every night until they were found by a police search party.
He was sentenced that time to 9 1/2 years in prison. His convictions included six counts of rape and one of abduction.
In 1997, Lihou went to live with one of his tutors after being released from jail.
After she asked him to leave because of his behaviour, he grabbed her, tied her hands behind her and forced her into a car.
A jury found him guilty of two counts of kidnapping but was unable to agree on whether he offended against the woman sexually.
However, a judge later concluded that the "signature" linking the crimes involving all three women was "forced sex during abduction".
After Lihou abducted the girl in 1988, a Court of Appeal judgment detailed his early life.
It said he had been led into early delinquency by "unsatisfactory and at times violent parenting" and made a state ward at 10 years old.
He spent most of the next five years in Social Welfare homes, often running away and offending while achieving little at school.
He was sentenced to corrective training at age 15, but escaped, was caught and sent to prison.
He was at that time dominated by feelings of anger at his unhappy and deprived childhood, and his rejection by society as a young adult, according to a Court of Appeal judgment dated June 28, 1989.
He had considerable difficulty in forming and maintaining normal personal relationships.
"It seems that without intensive psychotherapy he will be unable to cope outside institutional life," the judgment said.
When he was sentenced in 2013, Lihou was given a non-parole period of nine years and four months, meaning he will be able to apply for parole from late this year.
