About 400 schools were asked for their views just after the annual independent schools' census showed that the decline in boarding was the smallest for a decade.
Boarding numbers have been shrinking steadily. Parents appear to be increasingly reluctant to send their children away from home, cuts in the armed services have meant that fewer service children are sent to board and the recession has led to more families choosing the cheaper option of day schools.
A generation of parents who suffered cold showers and fagging has proved difficult to persuade that boarding life has changed. But Isis says that the pattern may be shifting as parents get the message that schools have become less rigid and austere. Returning economic confidence has also helped.
The survey found that 36 per cent of schools had received more visits from prospective boarding parents this year, while 19 per cent had received fewer. Even more - 43 per cent - reported more parental inquiries about boarding while 16 per cent reported fewer. Head teachers at most schools where boarders were much more confident about the future than those where only a minority of pupils board.
One of the reasons for the revival in boarding may be the growth of flexi- boarding which allows pupils to sample boarding for one or two nights.
Robin Lewis, head of Terra Nova school in Cheshire, said that Dinner Party Night, in which as many as 30 extra boarders spend the night at school with popcorn and a widescreen video while their parents go out, had proved an outstanding success.
He added: "It helps to ensure that we keep Saturday school and as soon as they discover boarding, many of the children agitate to become boarders themselves. We have a very high conversion rate."
Belmont, the co-educational prep school for Mill Hill School in north London, closed its boarding house 10 years ago but is opening a new one in September. John Hawkins, the head, said there was demand for weekly boarding from single parents and from families in which both parents led busy lives.
"It means they can feel secure that their children are in the care of our teachers rather than leaving them with nannies."
David Woodhead, the director of Isis, said: "It is too early to claim a full-scale boarding revival. There is considerable regional variation and many schools are still feeling the effects of a long and debilitating decline in demand. But the message about modern boarding is clearly getting through to more and more parents."
The revival is most marked in the south-east and, to a lesser extent in the South-west, and least noticeable in the North, the survey shows.
The private roll call
nSchools with boarders 1996: 829.
nTotal pupils 1985: 126,000.
nTotal pupils 1996: 90,000.
nTotal of boarders from service families 1988: 22,000.
nTotal of boarders from service families 1996: 10,000.
nPrep school fees: From pounds 2,200 per term to pounds 3,150.
nSenior school fees From pounds 2,600 per term to pounds 4,500.