Missouri business executive David Humphreys said the allegations were too damaging.
"At some point, you have to look in the mirror and recognise that you cannot possibly justify support for Trump to your children - especially your daughters," Humphreys was quoted saying in the New York Times article.
Another article revealed two major donors had asked for their money back and said they could not "support a crude sexist man."
It was not clear if Robertson had asked for his financial contributions back. He could not be contacted by the Herald on Sunday.
In 2010 Robertson was made an Honorary Knight Companion of the New Zealand Order of Merit for services to business and philanthropy. He owns a number of valuable properties, including Kauri Cliffs Lodge in Northland, Matakauri Lodge in Queenstown and The Farm at Cape Kidnappers and several wineries.
The family set up the Robertson Foundation, a programme that encourages university graduates into teaching for two years.
With his late wife Josie, Robertson gifted 15 paintings to the Auckland Art Gallery on their deaths.
The paintings by Picasso, Gauguin, Cezanne, Matisse and Mondrian, are worth $115 million.
One of his sons, Jay, has lived in Queenstown with his New Zealand wife, but they are currently in New York.
In an earlier interview with the New Zealand Herald Julian Robertson said receiving the knighthood was a special moment.
"It was a very emotional experience for me because New Zealand was a real love affair between my wife and me and the country," Robertson said.
