65-year-old Graham Roskell from Kirk Hammerton was reported missing on the morning of Saturday 3 November 2012, after leaving Harrogate District Hospital where he was receiving treatment.
He has not been seen since and there has been growing concern over his whereabouts over the past few days.
Mr Roskell's son started a campaign on Twitter when his father did not come home, and Graham Roskell was reported missing on Saturday.
North Yorkshire Police are now urging people to check their sheds, outbuildings and garages in case Mr Roskell has taken shelter in them over night.
Mr Roskell is white, with a stocky build and short grey hair.
He was last seen wearing a green patterned jumper, grey trousers and black shoes. It is also believed that he has a blue dressing gown with him.
Anyone who can help locate Mr Roskell is urged to contact North Yorkshire Police on 101 - select option 2 - and ask for Harrogate police.