This week just 164 pupils returned to the 11-17 co-educational school, built to take in 1,200. Parents of 11 to 15-year-old pupils have been advised by the Gravesend school to find alternative places for their children.
In a consultation document on the school's future, the FAS said: "Public statements have placed considerable pressures on the school, especially in the last year. In particular they have affected parental confidence, as shown by a fall in pupil numbers, and raised uncertainties about its future."
In January 1995, Southfields - which opted out five years ago - had 576 pupils on roll. By the beginning of this year numbers had fallen by 139.
Government inspectors have visited the school regularly since it was placed on special measures in March 1995 and reported steady progress.
This year for the first time some of its pupils gained a university place.Three-quarters of its sixth-formers who took advanced courses gained distinction. At GCSE 9 per cent of pupils gained five or more top grade passes against a predicted 3 per cent.
But, said the FAS: "Despite the progress now being made on the educational front, the pupil numbers for September 1998 are again lower than the previous year and do not therefore show a return of parental confidence."
The falling role has had a significant impact on the school's budget, with governors predicting a deficit of around Pounds 500,000 by 2001.
A delegation from the school is due to meet Estelle Morris, education minister, next week.
And Clive Hemsley, headteacher, said: "I would have liked to have got the school through special measures. We will continue to do what we can to save the school because that is what parents want."
If closure is ratified by Education Secretary David Blunkett Southfields will not only be the first named and shamed school to close, but the first GM school to be axed. Its land and buildings would revert to the council.
Allan Craig, the National Association of Schoolmasters Union of Women Teachers executive member for Kent, said: " What is causing the closure of Southfields is not its exam results but Blunkett's policy of name and shame."