The family of a mother-of-five missing for more than a month say they are living a "never-ending nightmare".
Sarah Wellgreen was last seen near her home in New Ash Green, Kent, on 9 October. The 46-year-old was reported missing two days later.
Son Lewis Burdett said volunteer search parties had provided "comfort" and asked people to "please keep looking".
Her disappearance has been described as "out of character" and police are treating it as a potential murder.
Mr Burdett, in his first public statement since his mother disappeared, said: "The last month has been a never-ending nightmare and so distressing for our family.
"We would like to offer our heartfelt thanks to everyone who has helped with the searches, reposting social media appeals, putting up posters and sending in CCTV and dashcam footage to the police."
About 2,000 hours of footage has been received by police, while more than 1,300 volunteers have joined searches of the surrounding area.
"Please, please keep looking and re-posting the social media appeals," 22-year-old Mr Burdett said.
"Myself and my family really do appreciate everything that you are doing."
Officers have searched woodland near Bluewater shopping centre in Dartford and areas in Greenhithe near the River Thames.
Divers have also searched the River Darent in Dartford town centre, while the fire service has provided a drone.
The only item missing from Ms Wellgreen's home was her black iPhone 4, and there have been no new transactions on her credit or debit cards. Her car was also left at her home.
A man in his 30s was arrested on 16 October and released on bail until 16 November. On Friday, bail was extended until 16 January 2019.
Kent Police would not disclose what he was arrested on suspicion of.
Ms Wellgreen, who worked in a beauty salon in Portsmouth, is described as being white, about 5ft 7in tall, of medium build, with green eyes and straight brown shoulder-length hair.