The 14-year-old blindfolded the little girl with a Hello Kitty apron and promised her a 'chocolate' before raping her.
Earlier this year, he walked free from Cambridge Crown Court after receiving only a community order and continued to live just a few doors away from the family.
The case sparked outrage around the country after the judge blamed 'the world and society' because the boy was addicted to pornography.
And the sentence so incensed the girl's parents that they appealed for the teen to be punished with a harsher sentence.
They said the judge's comments had 'cheapened' their daughter's ordeal.
But the Attorney General's office has said the appeal will not be allowed to go ahead because the case was 'difficult to sentence'.
It said the Court of Appeal would not regard the sentence as 'unduly lenient' and the case will not progress further.
The victim's mother - who cannot be named for legal reasons – said they were resigned to the outcome.
"It is coming up the anniversary of the attack and we don't wish to drag it all up again," she said.
"Now the decision has been made, we cannot appeal. We are now going to move on with our lives.
"It is disappointing, but as ever our priority is our little girl and her happiness - we just have to move on.
"We want to keep her life normal, we don't want to reinforce the memory and we want her to remain as content as she is now.
"We hope it doesn't effect her relationships in later life."
The abuse took place at the girl's Cambridgeshire home in December last year - the first time her parents had let the teenager babysit the girl alone.
But Judge Gareth Hawkesworth let him walk free because he said the schoolboy, who regularly accessed hardcore pornography on his laptop, was just being impulsive.
The judge told him: "I believe you have become sexualised by your exposure to and the corruption of pornography. Your exposure at such a young age has ended in tragedy.
"It was the fault of the world and society." At the time, the boy, now 16, said: "I think my hormones took over."
The judge said: "I'm satisfied it was impulsive."
He imposed a five-year sexual offences prevention order - barring the boy from using computers or mobile devices to view porn. His progress and whereabouts will continue to be monitored by police for the next two and a half years.
Previously on Parentdish: Judge blames 'society' for teenager's rape of five-year-old