Peters, in turn, applied to the court to be discharged from bankruptcy.
Just before last Christmas, Associate Judge Abbott released Peters from bankruptcy, saying he did not believe there was sufficient reason to impose sanctions on the former property developer or that his discharge would create "an unmanageable risk to the business community".
The Official Assignee then took the matter to the Court of Appeal and filed papers with the appellate court in February.
It was seeking to have the High Court's decision set aside and Peters' bankruptcy extended for at least three years.
However, the Official Assignee is now dropping that fight.
"The Official Assignee confirms that a decision has been made to discontinue the appeal against the decision to discharge Jamie Peters from bankruptcy," a spokesman said.
The decision to call over the appeal follows Associate Judge Abbott releasing full reasons into his decision to discharge Peters.
The judge said the inferences the Official Assignee invited the court to draw could not stand against evidence given by those other than Peters.
Peters is still facing separate charges brought by the Official Assignee, including for allegedly concealing property.