The Criminal Cases Review Commission has received only three new enquiries from parents saying they were wrongly convicted of killing their children.
Angela Cannings' case sparked a review of cases
The Attorney General set up a review of sudden infant death convictions after Angela Cannings was cleared on appeal of murdering her two baby sons.
It was widely assumed dozens of parents and carers would challenge convictions based on disputed medical evidence.
But with the review nearing completion, the number could well be much smaller.
The Commission, which has the power to refer convictions back to the Court of Appeal, identified 28 cases where such an appeal could be made.
So far, just two parents have applied to the Commission to challenge their convictions with one other indicating they probably would.
These applications were only made in the last week, a Commission spokesman said.
It is now trawling its own files for potential miscarriages of justice, and is likely to re-examine a murder conviction from the mid-80s that it had previously refused to consider.
Ms Cannings was convicted of the murder of seven-week-old Jason in June 1991 and 18-week-old Matthew in November 1999 in April 2002, based purely on the opinion of three experts, including the now-discredited paediatrician Professor Roy Meadow.
Commission chairman Professor Graham Zellick told BBC Radio 4 Today programme of his surprise at the length of time taken for the first applications to come through.
"I have to say I have been astonished that it has taken so long for the first two or three cases to reach us and I have no idea why that is," he said.
A Commission spokesman said the two applications received so far related to the death of a baby girl in 2000 and the death of a baby boy in 2001.
A third application was pending after initial contact by a solicitor last week, he added.
Five of the 28 cases identified by the Attorney General are already being looked at by the Commission and include the case of Donna Anthony, given two life sentences in 1998 for murdering her two babies.
These applications were made independently of the review.
Professor Meadow said there was a 73 million to one chance of two children in the same family dying of cot death.
He became renowned for an observation in a book that became universally known as "Meadow's Law", which stated: "One sudden infant death is a tragedy, two is suspicious and three is murder, unless proven otherwise."
In December 2003 the Court of Appeal decided to overturn Ms Canning's murder conviction.
As a result of her case being overturned, the law was changed so that no-one can be convicted in a criminal case on the testimony of expert witnesses alone, without referring to physical evidence.
And Mrs Cannings' experience led to reviews of cases in which children have been taken into care on the basis of disputed medical evidence.
Ms Cannings' first child, Gemma, also died of cot death in 1989, but no charges were brought in relation to that death.