Janet McQueen left her dog, mobile phone and money at her flat in Langside Road in the Govanhill area of Glasgow on 18 October last year.
Police said that despite door-to-door inquiries and numerous appeals there had been no trace of her since.
They said the past four months had been a "horrible" and "very distressing" time for her family.
Insp Alex Hutton, who is leading the search for her, said that on the day of her disappearance she was reported to have been acting in a distressed state on a bus.
He said: "This is a horrible time for the family; they just don't know where Janet is or what, if anything, has happened to her.
"The family kept in touch with each other and for Janet to be out of contact for so long is concerning and very, very distressing for them."
Mrs McQueen left her flat at about 21:00 Tuesday 18 October, leaving behind her dog Palsy, phone and money.
Insp Hutton added: "We know that earlier in the day she appeared somewhat distressed whilst travelling on a bus, so much so that the driver called police and she was taken home to family, however, for whatever reason, she headed out around 9pm.
"While there is nothing at this time to indicate any suspicious circumstances or that anything untoward has happened to Janet, it is very unusual for someone to just disappear without any trace.
"Officers have trawled through hours and hours of CCTV looking her, and we've been liaising with her bank in case there has been any activity on her account but so far nothing."
Insp Hutton urged anyone with information about Mrs McQueen's whereabouts to come forward.
She is described as being 5ft tall, of slim build, with short black hair. When last seen she was wearing glasses, a black anorak and dark-coloured trousers.
Detectives have issued a fresh appeal to find a 58-year-old mother-of-three who disappeared four months ago.