In September 2009, district court judge Graham Hubble rejected an argument that the Commonwealth of Australia should have brought the extradition case, and not New Zealand Police.
Mailley appealed the decision to the High Court, but Justice Rebecca Ellis backed the earlier decision and the appeal was thrown out.
The Court of Appeal quashed the earlier decisions, ruling that the extradition should have been brought by the Commonwealth of Australia, and not New Zealand Police.
A new case was brought, which Mailley again appealed to the Court of Appeal.
Now in a new judgement, Court of Appeal judges rejected Mailley's case, concluding that his personal circumstances were neither "compelling" or "extraordinary".
Previous decisions had failed to take into account Mailley's mental health problems and the fact he also suffers from heart disease.
Medical reports showed that Mailley has attempted suicide on several occasions, while he also suffered from bipolar disorder and post concussion syndrome arising from head injuries.
Fresh evidence presented to the Court of Appeal at a hearing in February this year, stated that Mailley was diagnosed last August as having a tumour on his neck, suspected of being a secondary cancer spread from an unknown primary site.
But in the new ruling, appeal judges said that while Mailley's health problems and consequent suicide risk are "unfortunate", they are "not out of the ordinary".
"Further, there is no suggestion that the Australian authorities are not capable of dealing with these problems and the associated suicide risk."
They also rejected arguments that extradition will break up the family unit for Mailley who currently lives in Auckland with his wife and teenage daughter, and remove his social and medical support networks.
"We consider the interests of justice will be served by extraditing Mr Mailley to Australia to face trial there," the judges concluded.
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• The Word
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• CASPER Suicide Prevention
If it is an emergency and you feel like you or someone else is at risk, call 111.