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Rejecting the application, Lady Justice Rafferty said the sentencing judge had not "fallen into error" in what was a "difficult sentencing exercise".
She said that "mercifully" cases of the kind involving Rooke came before the courts "relatively seldom".
Rooke, 45, was jailed along with his wife Donna, 40, and son Jamie, 19.
Jamie Rooke admitted affray and a number of counts of causing actual bodily harm and was sentenced to four years custody.
Donna Rooke admitted a specimen count of battery and was jailed for four months.
At the Crown Court, Judge Peter Kelson said the family used Kinsella like a "punchbag" and treated him "like a dog".
He said: "'Man's inhumanity to man never ceases to shock."
After the hearing, Mr Grieve said: "This was a shocking case of exploitation of a vulnerable man by a family who abused and assaulted him on a regular basis.
"Mr Kinsella was tricked and trapped by people who posed as his friends and employers. In reality they were manipulative and exploited him.
"He lived in David Rooke's garage in appalling conditions and the abuse only came to light.
Leading judges have rejected a challenge brought against the six-and-a-half-year jail sentence handed out to an ice cream business owner from Sheffield who kept a vulnerable man like a "slave".
Three judges at the Court of Appeal in London dismissed an application by Attorney General Dominic Grieve over the "too low" prison term imposed in the case of David Rooke.
Mr Grieve had asked Lady Justice Rafferty, Mr Justice Cranston and Mr Justice Stewart to review the term to rule on whether it could be regarded as "unduly lenient".
Rooke forced Craig Kinsella, 34, to live in a garage where he suffered regular beatings and ended up scavenging for food in bins.
He was sentenced at Sheffield Crown Court in January after admitting false imprisonment and a number of counts of causing actual bodily harm.