A landlord whose tenants include a posh Auckland restaurant has lost its second attempt to stop an alleged brothel being run from their building.

Sale 33 owns a building on the central Auckland street of the same name, which houses upmarket eatery Clooney on the ground floor.

The owner went to the High Court last year, alleging David Simpson, an ex-solicitor and former bankrupt, and his wife Maria were running a brothel from a five-bedroom, loft-style apartment on the building's top floor.

Sale 33 alleged it was always intended a brothel would operate from the apartment and that this was not disclosed.

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The allegations were denied and Justice Susan Thomas last December refused to order that Maria Simpson's company stop operating the alleged brothel at the premises or cease any prostitution-related activity.

The judge was not satisfied she had the jurisdiction to make the order and believed the appropriate place for the dispute was the Tenancy Tribunal.

Even if she was wrong on that point, Justice Thomas said she was not satisfied there was a serious question to be tried and believed the overall justice of the case did not favour granting the injunction.

Sale 33 then went to the Court of Appeal, which this week also declined to grant the injunction.

Justices Forrest Miller, Graham Lang, and Mary Peters, said the lease for the apartment expired in six weeks time.

"There would be little point in issuing an injunction for such a limited period unless there was clear evidence that Sale 33 is continuing to suffer significant detriment from the activities being carried on by the respondents," the trio said in their decision on Wednesday.

"It appears that the only remaining issue of any substance will be the claim for damages based on pre-contractual misrepresentations made by the respondents.

There does not appear to be any real issue that the respondents made representations that were false. The real issue is likely to be the quantification of damages," they said.