New data shows about 2000 children on any one day are living in households where their parents have lost up to half their benefits because in most cases they have failed to turn up to an appointment.
Beneficiary advocates and researchers say the Government is being negligent towards these children by failing to track what's happening to them.
A beneficiary advocate Kay Brereton said a broken down car or a sick child could mean a missed appointment and a penalty or sanction imposed.
"I had contact from someone last week who had been sanctioned because they couldn't make it 30km to a training course, and there hadn't been any transport arranged like the case manager had talked about doing.
"Some of these sanctions are really unfair and these mothers and fathers, families have choices about whether they pay the rent or they buy food."
Figures obtained by Radio New Zealand show that on the 30 June, at least 1948 children were living in households that had lost up to half their income, including 13 families with six or more children.
The Social Development Ministry said it could not report the total number of children dependent on beneficiaries who were punished annually because its system was unable to calculate that.
In a written statement, the ministry's deputy chief executive Carl Crafar said people with dependent children never lost more than half their benefit.
When a person with children has been sanctioned for two weeks, their case manager makes a follow-up phone call to discuss their situation.
Eighty eight percent of clients "re-comply" within four weeks, but those parents who do not are contacted by Work and Income to make an appointment.
"We do not collate or report on family hardship as a result of sanctions at a national level. However this is monitored on an individual basis and noted on individual files, and our case managers will work with these individuals all the time."
In the year to the end of June, 23,066 benefit cuts were imposed on parents with dependent children, although some individuals may have been penalised more than once.
A spokesperson for the Child Poverty Action Group, Associate Professor Susan St John from Auckland University, said this suggested more than 40,000 children a year could be missing out.
"But we don't how they are affected. There's no accountability. We don't know how these children get fed when their parents lose 50 percent of their benefit, and there's no evaluation.
"Are sanctions effective in changing behaviour positively? Or does it just punish parents and children for no outcome?"
Labour Party social development spokesperson Carmel Sepuloni said the Government was being "negligent".
She said the minister had gone on record over the upcoming overhaul of Child Youth and Family about the need for more monitoring and reporting - but would rather not know apparently about the impact of welfare reforms.
"If the child needs to be the central focus, then why don't we have any reporting on the implications of things like welfare sanctions on children? It doesn't make sense."
Social Development Minister Anne Tolley declined to be interviewed.
But in a written statement, she said the government was focused on ensuring children did not grow up in benefit-dependent households by supporting their parents into employment.
"What we are addressing are the terrible outcomes for children if they grow up with parents on benefits. We know they are more likely to be on a benefit themselves, have poorer educational results and are more likely to be involved in crime."
Mrs Tolley said there were 38,000 fewer people on benefits compared to three years ago, with the number of children in a benefit-dependent household having fallen by almost 42,000.
However, veteran beneficiary advocate Sue Bradford, from Auckland Action Against Poverty, said more people were struggling to put food on the table or a roof over their children's heads.
"This government does not give a damn about the children of beneficiaries. It's penalising children for the crime of their parents being on a benefit or trying to access a benefit."
Sue Bradford said benefit cuts were driving families deeper into debt, mental and physical stress and homelessness.