Arts patron Dame Jenny Gibbs says the gallery's operating budget has been progressively cut from $12 million in 2012 to the current $6.9m.
"This does not even cover salaries and wages and the gallery is having to consider closing on one or more days a week.
"The $6.9 million grant to Auckland Art Gallery is a disgrace and completely unsustainable. Auckland Council should be ashamed," said Gibbs, a major supporter of the gallery.
The funding squeeze has also meant the gallery cannot afford to keep top staff.
Gallery director Rhana Devenport, who is overseas, told the Herald in May that Te Papa had "stolen two of my best ... well, it's offering them a lot more".
Gibbs said principal curator Zara Stanhope had also left for the Queensland Art Gallery.
Today, Stanhope said salary was not a reason for leaving and does not receive a larger salary at Queensland Art Gallery.
"My concern was that the gallery's decline in budget has made it impossible to produce an exhibition programme of substance, in quantity and quality, for the community in the coming years," she said.
Devenport is taking a "highly proactive approach" to corporate sponsorship, philanthropic and cultural grants, but Gibbs said raking around for help was no longer sustainable.
Chris Brooks, who heads the council's regional facilities arm, confirmed the budget cuts since the gallery reopened in 2012. He also confirmed options had been explored to close for one or two days of the week, although a way had been found to keep the doors open this financial year, he said.
After property costs, Brooks said the gallery's budget should be about $9m but budget cuts from council to Regional Facilities Auckland (RFA) had been passed on to the gallery.
He said RFA would be making a bid for more money for the gallery as part of the council's new 10-year budget next year.
By way of comparison, Gibbs said, the Auckland Museum received $28m and the Museum of Transport and Technology (Motat) $11m this year from Auckland Council.
Under their own acts of Parliament, the museum and Motat set a levy which the council pays. The gallery does not have its own act and cannot set a levy.
Gibbs, who was deputy chair of RFA from 2010 to 2016, said she accepted that Auckland Council is under severe financial constraints with huge expenditure required for transport infrastructure, waterfront development and other matters.
"Meanwhile, however, they are strangling the heart and soul of the city, the things that make people want to visit and live here," Gibbs said.
"This is a centre of cultural life of the city and a major attraction, where 60 per cent of visitors are from out of town or overseas," she said.
A spokeswoman for Arts, Culture and Heritage Minister Jacinda Ardern declined to comment, saying it was a matter for the council.
A mayoral spokesman said Phil Goff was aware of the gallery's funding request, which would be assessed alongside all other funding requests in next year's 10-year budget and consulted on with Aucklanders.