Thomas Phillips, 34, Jayda Jin, 8, Maverick Callum-Phillips, 6, and Ember Phillips, 5 have not been seen since Saturday.
The family's vehicle was found abandoned with waves crashing around the next day on Kiritehere beach and family raised the alarm with police on Monday.
A large scale search focusing on the beach, surround bush and coastline resumed from 7am today and involves an Eagle helicopter and the Coastguard.
Thomas Phillips' uncle Paul Phillips told RNZ the family was remaining positive and hoping he was just hiding in the bush, although the family did not know why he would have done that.
"We are not sleeping a lot at the moment obviously we are worried about what is going on and what is happening."
Phillips described his nephew as not only a dedicated father, but also an experienced bushman.
Phillips had been farming in the South Island when he met his wife and they had three children. After a break-up, he returned to work on the family farm and had been raising the children for three years, he told RNZ.
The children's mother was in the Otorohanga/Te Kuiti area, but Phillips had custody. The relationship between Phillips and the children's mother was "not that great".
The family could not think of anything specific that would have prompted him to run off.
"We think he has probably just gone to hide and look after the children."
He was a competent bushman and keen pig hunter. They were unsure whether he had any gear with him.
Paul Phillips said he had initially feared the worst, but after speaking with his brother and sister in-law he was now realised there maybe other options and they remained optimistic.
Meanwhile, the tight-knit farming community in the King Country was rallying together and helping with the search.
Waitomo mayor John Robertson told Newshub there was no good news this morning and although search conditions weren't ideal, they were okay.
"It's a very close-knit farming community in a reasonably remote part of the King Country."
People were getting more anxious as the time went on, but Phillips knew the area and the bush well, he said.
"There's a number of theories out there and the police are preparing the search accordingly, but the hope is they are on land and that's the hope we want to keep alive."
Police officers were out in force in Marokopa yesterday going door-to-door trying to find the family, who spent their time between the farm in the tiny seaside settlement and another property in Otorohanga.
Waikato West area commander Inspector Will Loughrin said they had genuine concerns for their safety, and family remained anxious for their return.
"This is out of character for the family and this is day [four] so you will see a significant amount of resource to bring Thomas and the kids home."
The search and rescue operation involved LandSar crews on the beach, its surrounds, as well as the Eagle helicopter and Fire and Emergency NZ staff operating drones in the air.
The Coastguard is also operating a plane.
Conditions at Marokopa had been "fairly rough" over the past couple of days and would likely be rough again today, but it was hoped conditions would settle by tomorrow.
