Officers have thanked local people who have tried to help, but say somebody may yet be able to provide a crucial clue to his whereabouts.
Arnold (pictured) was last seen around 11.30pm on July 6 at an address in Panbrae Road, Bo’ness.
He left the property at some point during the night and was reported missing to police on the morning of Friday, July 7.
Police are still conducting searches of the local and wider areas, and say this will continue for the foreseeable future. .
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Arnold is white, slim built with blue eyes and dark receding hair.
He is around 6ft 3” tall and has a north of Scotland (Shetland) accent, and has previously lived in Aberdeen and Shetland.
He is believed to be wearing blue trainers.
Chief Inspector Damian Armstrong, area commander for Falkirk, said: “I would like to thank those members of the public who have assisted us in our efforts to trace Arnold.
“Your work is very much appreciated and we are grateful for the support of the Bo’ness community.
“We would ask those who are continuing to search for Arnold to make sure they engage with police and in order to ensure they search safely are not going into any dangerous areas.
“I would also reiterate that we are still appealing for information on Arnold’s whereabouts.
“I would ask anyone who remembers seeing Arnold in the hours and days after Thursday, July 6, or recognises his description, to get in touch with us if they haven’t already done so.
“Your information may hold the key to tracing Arnold.”
Those with information regarding Arnold’s whereabouts are asked to contact officers at Falkirk Police Station on 101, quoting incident number 1022 of July 7.