The 74-year-old victim, from Warwickshire, was out walking when she was knocked down by one of the motorcycles on the B1257 Helmsley to Stokesley road, near the Clay Bank car park, at around 5.20pm on Sunday 29 May 2011.
Following the collision the two riders, who were travelling in the direction of Stokesley, stopped briefly a short distance up the road before riding off.
Extensive police enquiries to trace the two riders remain ongoing.
The woman suffered shoulder and ankle injuries and was admitted to the James Cook University Hospital in Middlesbrough. Following treatment overnight, she was discharged from the hospital on Monday 30 May and is fortunate to be making a good recovery.
Inspector Nick Wattam, of North Yorkshire Police’s Road Policing Group said: “It is very disappointing and disturbing that the two motorcycle riders involved in this hit-and-run incident have failed to contact the police.
“They knew that a woman had been knocked down and suffered injuries, yet they selfishly and illegally carried on with their journey without any concern for her welfare.
“This behaviour is totally unacceptable and I urge anyone who can identify one or both of these individuals to contact the police without delay.
Insp Wattam added: “The public appeal for witnesses and information has also been disappointing despite the coverage in the media.
“Again, if anyone recalls seeing the incident near the Clay Bank car park at around 5.20pm last Sunday, or remembers seeing two bikers on this stretch of the B1257 at this time, please get in touch.
“Thankfully, the 74-year-old woman who was knocked down is making a good recovery having been discharged from hospital on Bank Holiday Monday.
“However, we can’t escape the fact that this could so easily have resulted in a tragic loss of life.”
Anyone with information that can help the North Yorkshire Police investigation is urged to contact 0845 60 60 24 7, quoting the reference number 12110087827. Information should be for the attention of Traffic Sergeant Neil Campbell and Traffic Constable Lee Hauxwell.
Information can also be passed on anonymously to the independent charity Crimestoppers on 0800 555 111.