Mr Parsons travelled to Fort William by train from his home on Friday, September 29, 2017.
He cycled south along the A82 and was last seen at 11.30pm that night outside the Bridge of Orchy Hotel, from where he apparently continued south towards Tyndrum.
Extensive searches of the area were later carried out, involving mountain rescue, air support, dog teams and civilian volunteers - all to no avail.
Chief Inspector Drew Sinclair, Clackmannanshire area commander, said: “Our thoughts very much remain with Tony’s family, who have had to endure two years of not knowing where he is or what may have happened to him.
“We are determined to provide them with answers and we want to ensure people remain aware that he is missing in case they may have information which could help.
“Neither Tony nor his bicycle have been seen since leaving Bridge of Orchy two years ago.
“I would urge anyone who believes they may have information or perhaps may have seen a bicycle or cycling equipment which looked out of place to come forward.
“Please do not keep anything to yourself if you feel it is small or insignificant. Allow us to make that judgement.
“I would like to thank everyone who has assisted our enquiries so far.”
Tony is 5ft 9ins and stocky with short greying hair and a moustache, and wore glasses.
He has a tattoo of an anchor on his upper right arm and a tattoo of an eagle on his left.
He was last seen wearing a red waterproof jacket, a blue long-sleeved cycling top, a high-vis vest, fingerless gloves, with beige combat trousers and walking boots.
Tony was also wearing a silver and grey cycling helmet, and was carrying a silver and blue rucksack.
His bike is yellow-framed with black handlebars.
Anyone with information can to contact Police Scotland via 101, quoting reference 559 of 2 October 2017.