The managed isolation booking system is getting about 100 formal complaints each week.
MIQ is now considering a wait-list for peak times to more fairly manage the unrelenting demand - with people currently needing to reserve rooms about 16 weeks in advance.
Since the booking system was introduced in August there has been a bottleneck of people wanting to come home sooner and spending hours or days sifting the website for cancelled bookings or employing others around the world to do that for them.
When MIQ released June and July spaces two weeks ago the website crashed because there were about one million hits.
Ship engineer Alan Pearman said he'd given up trying to get back from his work in Australia on his six-week breaks, likening the MIQ booking system to "fans fighting over concert tickets".
It had cost him the opportunity to see his daughter's new house, spend Christmas with his family or be with his wife in hospital after she was in a serious car accident this month.
"I didn't even try to come home because unless you're on death's door, you're wasting your time. That's been distressing, not being there to support her," he said.
After RNZ heard from dozens of upset New Zealanders overseas last year - including people who had been waiting days or weeks to hear about their emergency allocation applications to see dying loved ones - it requested a copy of the formal complaints sent to the Ministry of Business, Innovation and Employment, under the Official Information Act.
The ministry refused the request due to the substantial work needed to collate the data.
"The MIQ resolutions team can estimate that MBIE currently receive approximately 100 complaints each week relating to MIAS/allocation vouchers/special allocations," it said.
Immigration lawyer Richard Small said he wasn't surprised. He felt the way the system was "inequitable" because people who don't have money or free time can miss out on the dates they want.
"Somebody with an unwell relative who might be focused on their care is comparatively disadvantaged," he said.
He wanted to see people prioritised and put on a waitlist for rooms - which MIQ's deputy chief executive Megan Main confirmed was among the options on the table.
She said each complaint is acknowledged, reviewed and used to make improvements to the system.
"We've made some changes recently to prevent people from booking multiple vouchers, and we've changed the way we release vouchers to cover different time zones. At the moment, we're looking at the potential for a wait-list type situation, to help in periods of peak demand. So absolutely, we'll continue to improve it as we go forward," she said.
Asked if hours spent trawling the website for spaces is the way the system is supposed to work, Main said MIQ was still seeing more demand than there were places.
"While demand is exceeding supply, we'll always have that pressure. We'll always have those people that are really desperate to come back to New Zealand," she said.
About 20 percent of the complaints are about people's emergency allocation applications, to skip the queue for the border hotels.
MIQ gets about 160 of those each week from people who think they meet the strict criteria and it declines more than half.
"Just recently we added some information to the MIQ website about what evidence we need for emergency allocation, because we had complaints that people weren't clear about what was being asked of them," she said.
"We want to continue to learn, to improve from the feedback that we get."
Main noted that some people use the complaints form to send compliments to MIQ staff.
However, National's spokesperson for Covid-19, Chris Bishop, said people desperate for change were also taking their feedback to higher levels.
"There wouldn't be an MP in the parliament who doesn't receive regular complaints around the way the MIQ system works. We've simply got to do better," he said.
Asked what improvements he'd like to see, Bishop said the introduction of a travel bubble with Australia was the first step, because it would significantly ease the pressure on MIQ.
However, he said "a little will and pragmatism" was also needed to make the booking system better.