The 85-year-old vessel left the Bay of Islands on May 29 and was headed for Newcastle, Australia.
Neither the yacht nor the seven people on board have been seen or heard from since June 4. A search was launched on June 25 but was called off on July 4.
The Nina is owned by professional captain David Dyche III, 58, and his wife, Rosemary, 60. They were on board with son David Dyche jnr, 17, and fellow Americans Evi Nemeth, 73, Kyle Jackson, 27, and 18-year-old Danielle Wright. Also on board was Briton Matthew Wootton, 35.
Family and friends of those on board have refused to give up hope, despite the official search being called off. They have been fundraising to pay for private searches to continue.
``It is either that the Nina and its resilient crew got caught in a perfect storm, which caused everything to go wrong at the same time and orchestrated the sinking and total disappearance of a 21m yacht along with its seven-strong crew; or they lost communications, have damaged sails, and probably faced more damage that prevented them from making it to the shore since they left New Zealand,'' a representative of the families said on the official Nina Facebook page.
"When valuable human lives are at risk, there is not much of a point to the debate of which scenario is the more likely. It is only our duty to explore the possibilities.
"Can the boat be so crippled that the wind and the ocean currents dictate where they go? Or perhaps they still have some control and are making their way slowly to a shore ... Are they shipwrecked, waiting for rescue on a desert island or even on a reef? Or are they in the liferaft, still, hoping for a miracle?
"With all these possibilities in plain sight, to declare the Nina sunk and its seven human lives expired seems not only a bit irresponsible, but also insensitive.''
The families of those missing pleaded for help to keep their search going and said they would not give up hope.
The Nina families earlier criticised the official search, involving authorities from New Zealand and Australia, saying it was called off prematurely.
- additional reporting Anna Leask
