She was convicted in April 2015 but the High Court in September quashed the conviction and substituted it with a charge of ill-treating an animal.
The High Court ruled there was insufficient evidence to establish Power had acted recklessly when ill-treating Pip.
The case was sent to the District Court for re-sentence and in February this year, the lower court disqualified her from owning or exercising control over all animals, except 81 of various types, for eight years and was ordered to pay SPCA $6122.
About 60 animals were forfeited to the SPCA. She appealed to the High Court against the District Court sentence in May this year but lost. Power then applied for leave from the Court of Appeal to appeal the High Court rulings from September and May.
It was her second appeal against conviction. She argued both the District and the High Courts made errors of fact regarding the causes of Pip's death.
But the Court of Appeal declined leave, saying her appeal did not involve a matter of general or public importance and there would be no risk of a miscarriage of justice if leave was refused.
Auckland SPCA chief inspector Greg Reid said the process of uplifting animals from two properties Ms Powers owned in Northland had already started and was ongoing. He was not sure how many animals she owned.
"The challenge we have is every time we go to her properties, different animals pop up. But we're quietly getting there.
"So far we have removed sheep, cattle, llama, dogs and cats and we anticipate this will continue as we move towards ensuring Ms Power maintains a holding of animals in keeping with the judgment," he said.
Mr Reid said SPCA intended to rehome all the animals it could. Some animals may require treatment and rehabilitation prior to rehoming, while some animals such as cattle may have to be sold.