George Glackin, 43, from East Kilbride, South Lanarkshire, was last seen leaving his sister's house in Shettleston, Glasgow, on the evening of Monday September 17 to go to work as a construction supervisor.
He did not return the following morning, but was captured on CCTV in the Saltmarket area of Glasgow later that day.
Since then, there have been no sightings of the father-of-three, who also has two stepchildren from his current marriage to wife Karen Glackin, 49.
He was reported missing to police on Thursday September 20.
Police say Mr Glackin, who is known to friends as "Big Geo", is vulnerable as he has a number of conditions and takes daily medication, which he does not have with him.
He is also partially sighted as he has an artificial right eye.
Today, officers from Strathclyde Police interviewed members of the public around the Saltmarket, where Mr Glackin is known to frequent The Spirit pub and McKinnon's bar.
They released CCTV images of Mr Glackin in McKinnon's on Tuesday September 18, and also a new family photograph of the missing man.
Superintendent Steven Reed, from London Road Police Office, said: "As time passes we are becoming increasingly concerned about George's wellbeing.
"He requires daily medication and we know that he has not taken this with him.
"Although George had been known to take himself off for a few days in the past, he would always make contact with his family and has never been away for this length of time.
"We know he has access to a mobile phone but no contact has been made to any of his family members which is very unsettling.
"We also know that he has access to money but to date he has not used his bank cards.
"Our 'stop and interview' operation is an effort to jog the memories of people who may have been in the area of the Saltmarket on Tuesday September 18, 2012."
Last week, Mr Glackin's family made an emotional appeal for information about his whereabouts.
His brother Ronnie, 47, said: "George, we all miss you and want you to come home.
"Also, if anyone else has seen George in the last couple of weeks, please tell the police.
"We love you and miss you very much, and just want you to know we love you and to know you're okay."
Mr Glackin has short black hair which is greying at the sides, a moustache and was last seen wearing a knee-length black parka jacket with a red hood, blue jeans and white trainers.
Anyone with information should contact police on 0141 532 4600.