Bromley's latest appeal bid, which took him to the High Court of Australia, claimed testimony provided by the prosecution's central witness Gary Carter was unreliable.

Fresh psychiatric and psychological evidence around Mr Carter's schizoaffective disorder meant there was an "extremely high likelihood" that his account of events was inaccurate, Bromley's lawyers argued.

But in a split 3-2 decision, a majority of the bench - including Chief Justice Stephen Gageler, Justice Jacqueline Gleeson and Justice Jayne Margaret Jagot - dismissed his application for special leave to appeal on Wednesday. 

In doing so, the court upheld a decision by the South Australian Court of Criminal Appeal that the new evidence was not compelling and not in the interests of justice to hear it at trial.

"We see no error in the Court of Criminal Appeal's reasoning and agree with its conclusion," the judgment said.

The judges found the fresh evidence was "not highly probative" in the context of Mr Carter's reliability in identifying Bromley as the man who attacked Mr Docoza.

But in a minority judgment, Justice James Edelman and Justice Simon Steward found there was "a substantial miscarriage of justice" because the trial judge gave inadequate directions to the jury.

They argued Bromley should be acquitted without a retrial, given the loss of original evidence and the length of time he had spent in prison.

"There is, at least, a significant possibility that an innocent person has been convicted," Justices Edelman and Steward said.

Bromley has been in prison since 1985, having been denied parole because he has maintained his innocence throughout.