Three judges at the Court of Appeal will consider their case following a defeat at the High Court in London in August.
Mrs Maguire's husband Don, children and nephews wanted Mr Justice Holroyde to order the decision taken by assistant West Yorkshire coroner Kevin McLoughlin to be reconsidered.
But the judge dismissed their application for judicial review.
The 61-year-old teacher was stabbed in the back by 15-year-old Will Cornick as she taught a Spanish class at Corpus Christi Catholic College in Leeds in April 2014.
The Pope led the tributes at the time of her death.
Cornick was later sentenced to life with a minimum term of 20 years.
An inquest into Mrs Maguire's death is due to take place before a jury at Wakefield Coroner's Court on November 13.
Mr Justice Holroyde said when he announced his decision: "I have much sympathy for the claimants, and I fully understand their reasons for wishing to pursue this line of inquiry."
But he said he was "unable to accept the submission that the assistant coroner reached a decision which was so seriously flawed as to be... unreasonable".
During the High Court hearing, counsel Nick Armstrong told the judge it was the only occasion on which a teacher had been killed by a pupil in a British classroom and the family were anxious "that all the lessons that can be learned from this enormous tragedy are learned".
Yogi Amin, a partner at law firm Irwin Mitchell who represents Ann's family, said: "This appeal represents the next step in the family's long running battle to attain a full and fair inquest in to the murder of Ann."
