The bar applied for the license to allow it to offer dancing as well as live music, but was told that the application, if granted, would breach council policy because the bar was close to homes.
Councillor Jeane Lepper, who chairs the city’s licensing committee, said no compelling case had been made to breach policy and added: "There would be an increased potential for noise".
Doug Simmonds, speaking for the Candy Bar, objected that it would not set a precedent and the bar was not asking to stay open longer.
Simmonds added there had been no complaints about the bar, which has been open for two years.
The Candy Bar’s sister outlet in Soho, London, has a license until 2am on Friday and Saturday nights.