The 59-year-old was last seen by his landlord on October 5 at his home on Waihoanga Rd. He left his car and other personal items at the property before he vanished.
Hill has limited mobility due to a back injury so police have been focusing their search in the area of his home.
But last week they widened their probe to include steep and bush-covered terrain.
Detective Senior Sergeant Dave Thompson said there are concerns Hill would have run out of his health medication, which he needs on a regular basis.
“This is a distressing time for the family, who are looking for answers on the whereabouts of Duncan. We believe he is still in the area of Waihoanga Road, but the terrain in some areas is very rugged. The Ōtaki Gorge is also an area of interest for us.
“We are still keen for any sightings of Duncan in these areas around October 5 and encourage people to come forward with anything they feel is relevant.”
Police issued a statement on behalf of Hill’s family who thanked authorities and volunteers involved in the search.
“Everybody is putting a tremendous effort in to find Duncan in rugged, remote and challenging terrain, for which we are truly grateful.
“This is an extremely distressing time for our family and friends, as we are desperate to find out what has happened to Duncan.”
Hill is known to spend periods of time alone or in the company of spiritual groups, but police and his family would like to hear he is safe.
He is described as being caucasian, with greying hair.
He is 185cm tall (approximately six feet) and of a stocky build.
