Son Edward, who hopes to start a dairy and beef farm, described the decision as madness.
He said: “It is an extreme case of bureaucracy gone mad.
“We need the immigration minister to understand this case is absolute nonsense and use the power available to him to grant the application.
“We came here legally, we haven’t submitted false documents, and we haven’t committed any crimes. In any other walk of life or business it just wouldn’t happen.”
Mr Talbot, now 62, first visited Dorset 42 years ago when he travelled over from New Zealand and spent a year working on a farm.
The couple, who have been married or 32 years, now live in a farm cottage near Blandford Forum.
The family’s GP wrote a reference for them, saying they were “honest, hard-working and reliable”.
The doctor added that the stress of the “unfair” situation had caused them health problems.
The Home Office has not commented on the situation.