Mrs Gray said Mr Brown's position was as a figurehead, and his only engagement this year had been speaking at an event earlier in the year celebrating the service's 120th anniversary.
The community-based counselling service caters for individuals, couples and groups seeking help for trauma, anxiety, abuse, relationship difficulties, grief and addiction.
It operates from three offices in Mt Eden, Northcote and the Hibiscus Coast.
Alan Brookbanks - the council's human resources director - is also the chairman of the board of the organisation.
Yesterday the mayor said he was grateful for the board's support and understanding and that he was very much supportive of the work they do.
Despite the organisation's support for Mr Brown, a south Auckland pastor whose church has been visited by him says it is unfair that the mayor stays in the role.
Manukau New Life Church pastor Stephen Miller said he was deeply disappointed when revelations of the sex scandal broke last week.
Mr Brown visited his congregation - including a large number of young people - and spoke about his life.
"It's been really interesting to read about ... not just the mistake, but the two years of really what has been deceit towards his wife and his family.
"To me, unfortunately Len Brown has lost a lot of credibility. Yes, there is forgiveness. But if you're going to be the leader of our city and those sorts of organisations - particularly one that's talking about family - you've got to live it."
Mr Miller called on the Home and Counselling group to look for another leader. He acknowledged compassion and forgiveness were huge values preached in the church.
"There is compassion and there's forgiveness, but then there's also consequences when you step into a role of leadership. I'm a leader of our church. If I were to do something like that - to have an affair with somebody - I'd acknowledge that and ask for forgiveness too.
"There'd be compassion, but there's no way I'd be staying in my role as leader of the church. Because people have to look up to you as a leader and know that they can trust you and know that you have integrity and that you're not saying one thing and doing another."
Mr Miller said when Mr Brown won the mayoralty for the then Manukau City Council, members of his church youth group sent him a card and gift to enjoy with his family.
"We sent him a card and said to him: 'Now that you're the mayor of this city, we want to make sure that you look after your family. Because when you look after your family, everything else falls into place'."
Dr Camille Nakhid, who chairs the Auckland Council's ethnic peoples advisory panel, has criticised the media coverage of the affair.
The coverage, she said, denigrated, degraded and disparaged ethnic communities by shifting the focus from a white, heterosexual, middle-income, male lawyer with power to a female Hong Kong Chinese, part-time burlesque dancer with little power.
The consequences had been an outpouring of support for one and a lack of sympathy for the other "and that has a lot to do with the elite media in their representation of our ethnic communities'', she said.
Dr Nakhid said she was not concerned with the affair itself and did not condone the behaviour of Mr Brown and Ms Chuang.
She described Ms Chuang, a member of the panel, as one of the most supportive members and a team leader of the youth subcommittee.
Mr Brown has said he would not reappoint Ms Chuang to the panel.
