Stuart, 47, of Fair View Road, was last seen in the town at the end of August.
He was reported missing on October 14 after his family had grown concerned for his welfare.
Det Ch Insp Derry Crorken, of Lancashire Police, said: “Stuart’s disappearance is extremely worrying and we would urge anyone with information about his whereabouts to come forward.
“He has not been seen or heard from for more than two months.
“We know Stuart sent a message to a relative on social media on August 18. He suggested he had been given a job in the Lake District and would be working there.
“We’ve conducted a number of enquiries with Cumbria Police but have yet to find him.
“It’s crucial we try and establish where Stuart has gone to try and build a timeline of his movements. It is vital anyone who has seen him or knows where he is contacts us.
“Every day which goes by without finding Stuart is more and more concerning.
“We remain committed to finding him and have a large team working on the investigation.”
Stuart is described as white, 5ft 11ins tall, of medium build, with brown hair and brown eyes.
He has links to West Yorkshire, Cheshire and may have travelled to the Cumbria area.
Police have released several appeals for information to try and find him. There have been several reported sightings of Stuart in the Warrington area, including Linear Park, Culcheth, earlier this month.
Det Ch Insp Crorken added: “Stuart’s family has been left devastated by his disappearance.
“They just want to find him – any piece of information, however seemingly insignificant, could be crucial to locating him.
“Please take a good look at his picture too – have you seen him, or a man similar in description, in recent weeks? Call police if you can help.”
Anyone with information is asked to call police on 101, quoting log 1542 of October 14.