Rod Murdoch (71) was last seen about 9.30am on August 6.
Constable Nayland Smith, of Omarama, said there had been no reported sightings since.
''There's been nothing, no sightings, absolutely nothing,'' he said.
Mr Murdoch has various health issues, including delusions, is unable to walk unaided and is possibly suffering from dementia.
''He needs a Zimmer frame [or wheelchair] to get around. He's fairly immobile,'' he said.
His family were becoming increasingly anxious to establish his whereabouts and police had ''serious concerns'', Const Smith said.
Mr Murdoch is believed to be driving his green/silver 1994 Toyota Hilux Surf, registration number CHW194.
It is believed that he had about three quarters of a tank of fuel in the vehicle.
He may also have his dog - a grey and white giant schnauzer - with him.
''His dog was definitely seen getting back in the vehicle with him,'' Const Smith said.
Support from the Omarama community to assist in ground and aerial searches for Mr Murdoch had been ''incredible'', Const Smith said.
''The Omarama township has just all got together. We've been inundated with support,'' he said.
The Omarama Aero Club had dispatched planes for aerial searches of the area on Saturday and yesterday, Const Smith said.
Another pilot in Hawea had also volunteered his time to do an aerial search of the Hawea area.
