The Clinton Lions Club member never returned home to Romahapa after a meeting in Clinton on Wednesday night and an extensive search has been under way since his wife reported him missing at 1am on Thursday.
In a statement to the Otago Daily Times, family spokeswoman Julia Mathieson said the family was ''extremely grateful'' to ''all the people who have helped in the search''.
And she asked farmers in the wider area to continue to check their properties for any sign of him.
''As time goes by we start to face the inevitable that Ian will not be found alive but we have not given up hope,'' she said.
''It is very frustrating and worrying not knowing what happened to Ian. It is like he has vanished into thin air.''
Police believe the Romahapa man became disoriented on his way home and got lost.
His car was found abandoned in a paddock on a Carterhope farm.
It was mired in mud and footsteps led away from it.
Senior Constable Murray Hewitson, of Owaka, said many had offered to help in the five-day search.
''The whole community has got behind it,'' he said.
''Everyone's just offering their help.''
But he said the search was unlikely to continue today.
The police national dive team, enlisted at the weekend, had ''come up empty'' in the search of Kaihiku Stream on Sunday and yesterday.
At the end of Sunday night, more than 2500 man hours had been spent on the search and in total 7000ha had been searched, Snr Const Hewitson said.
The 28sq km search area had been searched repeatedly and multiple helicopters had been used, as had a drone, specialist search dogs, water rescue teams and LandSAR crews from Dunedin to Tokanui.
Yesterday, the search was extended to roads leading to Balclutha and Romahapa from the 3000m radius around Mr Mathieson's black 2009 Nissan Maxima where the search had been centred.
Some areas were searched for the fourth time yesterday ''just to be sure we haven't missed the smallest little something'', Snr Const Hewitson said.
But searchers had few solid clues.
''Every minute that goes by that we haven't found him is certainly frustrating us,'' Snr Const Hewitson said.
The search would be reviewed and peer-reviewed.
''We want to know that we've done the best possible job for Ian as well,'' he said.
The Mathieson family thanked ''New Zealand police, the search and rescue teams, members of the Lions Club, local farmers and private individuals who have donated money resources and their time to support this huge effort''.
Clinton Lions Club president John Whiteside said Mr Mathieson was a valued member of the community.
He had been a valued member of the Clinton Lions Club for a long time.
A large number of Lions Club members were involved in the search for Mr Mathieson.
''He has made a huge contribution to the community over the years,'' Mr Whiteside said.
