Eddie and Natasha Batha's daughter Mia was born with Down's Syndrome.
The number of Down's syndrome pregnancies has risen by more than 70% over the last 20 years, University of London researchers say.
The sharp rise reflects the growing number of older women becoming pregnant, when there is a higher risk.
An increase in the number of subsequent abortions and more antenatal diagnoses means slightly fewer children are being born with Down's syndrome.
Campaigners say better education about the condition will reduce abortions.
The number of Down's syndrome pregnancies rose from 1,075 diagnoses in 1990 to 1,843 by 2008 in England and Wales.
Despite the higher number of Down's pregnancies, the number of babies with Down's syndrome has fallen by 1%, from 752 to 743.
This is because improved antenatal screening means more Down's pregnancies are being spotted and more abortions are taking place. Without the improved screening, the number of babies born with Down's would have risen by 48%, according to the study.
A genetic disorder named after the British physician John Langdon Down, who identified it in 1866.
Inhibits the ability to learn and develop mentally.
About 60,000 people have Down's syndrome in the UK.
The proportion of couples diagnosed with a baby with Down's syndrome who decided to terminate has remained constant at 92%, say researchers at Queen Mary.
The risk of having a baby with Down's syndrome is one in 940 for a woman aged 30. But by age 40, the risk rises to one in 85.
Joan Morris, professor of medical statistics at Queen Mary, led the research and she said: "What we're seeing here is a steep rise in pregnancies with Down's syndrome but that is being offset by improvements in screening.
"It was thought that these improvements would lead to a decrease in the number of births with Down's syndrome. However, due to increases in maternal age this has not occurred."
Professor Morris said the Down's screening test had become more widely available over the last 20 years.
The report was published in the British Medical Journal.
Doctors told Natasha and Eddie Batha that there was a one-in-170 chance that their daughter Mia, who is now three, would be born with the condition.
Mr Batha told BBC Breakfast that their shock of learning that Mia did have Down's syndrome soon gave way to the realisation that the condition was not as bad as they feared.
'Another human being'
He said: "You're led to believe that it's the worst thing that could possibly ever happen to you.
"And then you realise it's just another human being who happens to be a little bit different.
"She just takes a bit more effort and she is a bit slower to pick up on things."
His wife agreed that many people were misinformed about Down's syndrome and she thinks this has contributed to the high abortion rate.
She said: "Because you have a test [during pregnancy] you think that it must be a terrible thing if it happened.
"There's no qualifying information and I think that would be really useful to get that and it might affect a lot of people's decision as to whether they could live with that."
Carol Boys from the Down's Syndrome Association said the number of abortions would be reduced if parents were better informed about Down's syndrome.
She said: "We realise that tests will continue to become more accurate at increasingly earlier stages of pregnancy.
"It is therefore even more important that families undergoing the screening process are given non-directive counselling and accurate, up-to-date information about Downs' syndrome."
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