Kim returned to New Zealand, where he has held permanent residency since age 14, in October 2010.
China requested his extradition seven months later, but because there is no extradition treaty between New Zealand and China, the request had to be dealt with by then-Justice Minister Simon Power.
Mr Power allowed the case to go to court, but an extradition hearing has been delayed while his lawyers challenge the legality of Kim's detention.
His latest appeal, against the decision to deny him bail, was struck out by the Court of Appeal yesterday.
The court said it did not have jurisdiction to hear the appeal because Kim had already appealed, unsuccessfully, to the High Court.
Kim's lawyer, human rights barrister Tony Ellis, said the case raised some "unique and important" human rights issues.
Chinese authorities have said they would not seek the death penalty if Kim was extradited, but Mr Ellis said that was among the issues.
"There's certainly evidence that people are tortured in China and we know they do have the death penalty, and whilst they might be claiming it's not going to be imposed, I don't think the assurance is worth the paper it's written on.
"And then there's also the question of whether he can get a fair trial in China, because neither the judiciary nor prosecution are independent - so there's some major human rights issues to come to grips with."
Mr Ellis was considering whether to appeal the latest ruling in the Supreme Court, or to lodge a new bail application in the High Court.
He was also considering taking the case before the United Nations Human Rights Committee's working group on arbitrary detention, which could hear the case while court proceedings were ongoing.
A judicial review of the case has been put on hold because Kim was denied legal aid and cannot fund an independent expert on Chinese law.
Mr Ellis said the extradition hearing, which would be held once the appeals to higher courts were complete, would be the beginning of a slow process.
"It could take another two years anyway - it's not going to be a quick process, whatever happens."
If Kim is found to be eligible for extradition it will still be up to Justice Minister Judith Collins to decide whether to surrender him to Chinese authorities.
Ms Collins could decide not to extradite Kim if there are grounds to believe he is in danger of being tortured or sentenced to death.
Human rights groups have criticised of the use of the death penalty in China, which executes more people a year than any other country where capital punishment is legal.