A professor of audiology, who was an advocate for the introduction of newborn hearing screening, says rigorous efforts must be made to track down all the children who weren't properly tested.
Mistakes by screeners, which included checking the same ear twice, triggered the recall of just under 7000 children for re-testing by 10 district health boards since December last year.
To date, 1751 of them have been re-screened.
An Auckland University professor, Peter Thorne, says it is very distressing for parents to know their children were screened, but now have to go through that process again.
Apology to parents from Counties Manakau District Health Board
The most recent DHB to uncover discrepancies is Counties Manukau, which has identified 963 children who may not have been properly screened, and Taranaki.
Counties Manukau's offer to re-test children was prompted by the identification of a two-and-a-half-year-old with significant hearing loss. The DHB says the toddler is now being treated for severe hearing loss.
The National Health Board says after analysing data collected prior to the period covered in its original review, it found a total of 10 DHBs had hearing screeners who failed to follow the newborn screening protocol.
The NHB says to date, five children whose hearing problems weren't originally picked up have since been diagnosed with hearing loss - two of those being severe to profound.
Counties Manukau has apologised to parents and children affected by the problem and says the current screening programme is robust.
David Grayson from that DHB says the case that prompted its rescreenings dates back to the end of 2010, and they are now checking all of the other cases tested by her.
Dr Grayson says she is no longer involved in the testing programme. "As I understand it, she feels that she was doing things correctly."
A chief advisor at the Ministry of Health, paediatrician Pat Tuohy, told Checkpoint they're confident they've weeded out all the bad screeners.
"We've been through exhaustive reassessments of all of the screens done by screeners across all of the DHBs and that's just been completed now. So we're pretty confident that this practice is now stamped out in New Zealand but it's been a steep learning curve for us."