Support helplines and inboxes were initially overwhelmed by demand from people grappling with online applications.
There were 70,000 calls to the 0800 helpline last Thursday alone.
The Ministry of Health has moved extra staff into technical support to run three call centres, and extended the centres' hours to 8pm.
Nearly 400 pharmacies are also now able to process passes, to reduce pressure on the phone and online methods.
Aucklander Ian Rushton would have liked that service available at the start.
After a few hiccups he got his pass online, but for many of his peers at retirement age, the website is in the too-hard basket.
"I know people in my age group who just don't even want to know about the internet and being online, it's just too foreign to them," he said.
"And then I know others who can kind of do their basics like their online banking and their email but anything new like this - a little bit out of their depth."
Monique Harvey has been one of those trying the lines repeatedly. When she attempted to download her pass, one of her doses did not show up.
"On Thursday I got through on the 0800 number, I can get through now, but the person there is unable to do it. They're forwarding a request to somebody to get the vaccination status changed."
She has found the wait "really frustrating".
"I've got an email from the events centre where I go to the pool and use the pool, and from December the 3rd I need to show a vaccine pass to go in there and I don't have one at the moment."
University of Auckland research fellow Dr Andrew Chen said a huge amount of work had gone into the Covid pass technology, and in many ways, it had surpassed expectations.
"It's government IT, which makes it even more likely to fail. The history is littered with examples of government IT projects that have just not managed to stand up or have had a lot of issues and errors.
He said the fact that it was rolled out to serve almost four million people in a matter of two or three months was "pretty amazing by government IT standards".
Despite the system being swamped at the start, Chen said it was good people were eagerly adjusting to Aotearoa's latest Covid-19 reality.