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The soft plastic recycling scheme, run by the Packaging Forum, has been operating since 2015 and now covers about 70 percent of the country, with further expansion planned.
The material being put in the bins in supermarkets had been going to a company in Australia, to be turned into things like park benches, bollards and playground equipment.
But the scheme's manager, Lyn Mayes, said the company wasn't taking soft plastic from New Zealand anymore, because it was getting too much.
Ms Mayes said the scheme had been looking for a local company to process it instead.
"We have actually signed a supply agreement with a new company and we'll be making some announcements around that very soon," she said.
In the meantime, a lot of that soft plastic is being kept in storage and stockpiled until it can be recycled, or it is being used in processing trials.
The scheme was also looking at other recycling options overseas, Ms Mayes said.
But she said they had found that processors had become a lot fussier about the quality of plastic they were being sent.
That meant people needed to be much more careful about what they were putting in the bins, Ms Mayes said.
"If people do put in metals, or coffee cups, or drink containers, then that will contaminate the whole bag."
Those bags would not then be collected.
Waste consultant Sandra Murray said part of the problem was soft plastic couldn't be sold to recyclers, unlike other materials, like PET plastic.
"That has a value, you can sell it to someone who wants it, but the soft plastic material doesn't really have much value at all, so either you have to pay someone, or not recycle it."
Ms Murray didn't think people would be too impressed their soft plastic was sitting in storage, waiting to be recycled.
"If people have gone to all this effort, they have an expectation that it is going to be recycled, but if it's just being stockpiled, that's not what people are expecting is going to happen, and if it ends up in landfill because there isn't a proper recycling outlet for it, then that's not what people were expecting either," she said.
Last year, 365 tonnes of soft plastic was collected by the recycling scheme.
That figure was expected to grow to 600 tonnes this year.
The soft plastic recycling scheme got some initial funding from the government, but it is now fully funded by the packaging industry.