Schools which fail to improve within six years of being classed "satisfactory" should be re-labelled inconsistent and pushed harder to improve, a report says.
The Royal Society of Arts report says half of the 40% of England's schools classed as "satisfactory" failed to improve within two Ofsted inspections.
Last month Ofsted said nearly 800 schools were "coasting" in this way.
The report says such schools are more likely to be in poorer areas.
The RSA report, published jointly with Ofsted, focused on the 40% of secondary schools in England rated as "satisfactory".
It noted that half of these schools remained "satisfactory" for at least two inspections and about 8% declined to an "inadequate" rating.
The figures also showed that disadvantaged pupils were more likely to attend "satisfactory" schools than their more affluent counterparts, with a higher proportion in Yorkshire and Humber, East Midlands and the East of England.
"Satisfactory" schools in more affluent areas are also more likely to be able to improve performance and achieve a "good" rating in subsequent inspections.
The report author, Professor Becky Francis, said: "Given the larger proportion of 'satisfactory' schools compared to failing schools, they are having a more widespread impact on outcomes for disadvantaged children than are failing schools.
"It's really urgent that this issue be addressed. These schools need to be directly supported to improve and to be held accountable for doing so."
She added: "It seems to me to be genuinely quite preposterous that we have a very high quality inspection system but very little framework to ensure schools improve."
The issue of "coasting schools" has recently been highlighted by the prime minister and by Ofsted's incoming chief inspector, Sir Michael Willshaw.
Sir Michael said he wanted to replace the word "satisfactory" in Ofsted inspections with a clearer explanation of why a school could not be called "good".
A spokesman for the Department for Education said it agreed with the thrust of the report.
He added that from January, a tougher inspection regime would be targeting schools at risk of falling back or making slow or no progress.
'Playing with labels'
The RSA suggested heads of "satisfactory" schools should be be required to draw up plan outlining how areas of weakness would be addressed, and to submit regular updates on progress.
It is also advocating a new nationwide support system to help teachers share best practice.
Russell Hobby, general secretary of the National Association of Head Teachers, agreed that schools needed help to focus on teaching quality but he questioned whether pay cuts would help attract the best into the profession.
He said: "We welcome the recognition that support must accompany challenge... where extra work is required it must be recognised.
"Let's not waste any time playing with labels - the goalposts change all the time and the inspection process is inconsistent - let's just help every school on its journey to being great."
Brian Lightman, General Secretary of the Association of School and College Leaders, said it was "seriously misleading" for Ofsted to interpret the term satisfactory as the opposite of its dictionary definition.
"If they mean unsatisfactory they should say so.
"The distinction between 'good' and 'satisfactory' should be abandoned and there should be three grades: above expected level of performance, around expected level of performance and below expected level of performance."