A Wellington city councillor has called Mayor Tory Whanau an "embarrassment to the city" and given her thoughts on whether the mayor should keep her job after Whanau admitted to a drinking problem.

Whanau has had a second public incident involving alcohol in recent months after being spotted intoxicated at a Wellington bar two weeks ago. She responded by claiming she is a “flawed” person but was getting professional help.

But councillor Nicola Young has told the Mike Hosking Breakfast that Wellington can't go on hold.

"Clearly, Tory is not well - which is sad," she said when asked what needed to be done in response to Whanau's confession.

"She has to look after her health, it's a top priority."

Young revealed Whanau had been "largely absent" from the council recently, typically taking meetings via online video calls. Young also expressed misgivings about her judgments.

"Her behaviour has become an embarrassment for the city - I'm getting clear feedback she's lost the trust and confidence of Wellingtonians," said Young.

"The mayoralty isn't a job for somebody with an addiction issue."

But she said were the council to vote on Whanau's job security today, it would likely still back the mayor's job "because the Greens and Labour make up the majority of the council table".

It's an opinion that doesn't sit well with Young.

"We took an oath to put Wellington first and we have to put Wellington first, it's not about one person, it's about the future of our city."

When asked if Whanau's issue was known, Young responded: "Oh yeah, I think so. I mean, we've had incidents before, haven't we?"

Although Young believed the council had lost the trust of the voters and ratepayers, she wasn't sure if anything could have been done to prevent it.

She said Whanau had been noticeably distant from her fellow councillors and hadn't built strong relationships with those at the table.

"I've only had one five-minute conversation with her since she was elected over a year ago," said Young.

"I don't have a relationship with her. I don't know what her friends were saying but it's very sad."

Meanwhile, a second councillor said Whanau’s drinking problem explained why she has been missing in action and said they were concerned she might not be able to hold office.

It’s understood the latest incident happened at Wellington’s Havana Bar late in the afternoon of November 18, with media reports that she and another person were “visibly” intoxicated.

Cr Tony Randle said the issue has a major effect on her ability to do her job.

He said Whanau cancelled councillor-only meetings just weeks ago.

“I am sympathetic about Tory’s drinking problem, and it may explain her being increasingly distant from many councillors. But she has a huge job as mayor, especially when our city has so many major challenges,” said Randle.

“I am worried we will be making decisions about the city’s Long Term Plan and District Plan when the city’s leader is distracted by personal issues and not communicating with all councillors. Wellington will suffer."