Michael Slaven, 23, from Dumbarton, was last seen in the early hours of Friday after leaving the Sugar Cube nightclub in Queen Street, Glasgow. The last confirmed sighting was on CCTV footage in nearby St Enoch Square.
John Slaven, 52, said: "I haven't lost all hope of finding Michael, but it is becoming very difficult.
"It's getting to the stage now, where it is hard not to find someone who hasn't heard about Michael going missing, which is good.
"But we are no further forward and haven't had any new information, it leaves us wondering what else can we do to find him?"
Around 80 people gathered at St Enoch Subway station yesterday for the search of the city centre.
The missing man's uncle Vincent Slaven searched an area near St Andrews Cathedral, where his nephew is reported to have been seen at around 2.45am on Friday.
John Slaven, an estate agent, added: "We have been searching all over, but we are no further forward.
"We're concentrating on a half-mile radius from where Michael was last seen, as I believe he is still in that area.
"There has been around 20 minutes of CCTV tracking Michael in that area, but nothing since.
"Surely a camera would have picked him up if he left that area?"
Michael is described as around 6ft, slim, fair and is clean shaven with short brown hair and brown eyes.
When he was last seen, he was wearing a white T-shirt with a grey square emblem on the chest, olive green chino-type trousers and dark plimsolls.
Michael Slaven has not used his mobile phone or accessed his bank account since he was last seen.
It emerged on Tuesday that officers are checking claims Michael was last seen at St Andrew's Cathedral, in Clyde Street, on Friday.
He may have been injured climbing over a fence to get into the car park at the church.
A spokesman for the Archdiocese of Glasgow confirmed CCTV had been passed to police.
John Slaven said he is "positive" the CCTV images from St Andrew's Cathedral show his son.
He said:"He could still walk, but looked like he had maybe hurt himself. His arms looked limp."
His parents say he appears to have been acting erratically in the images and suggested his drinks may have been spiked.