The 32-year-old was jailed alongside her husband Mick at Nottingham Crown in April after the pair were found guilty of the manslaughter of Jade Philpott and her brothers John, Jack, Jesse, Jayden and Duwayne.
She lost the first round of a bid to challenge her sentence in July but judges sitting at Nottingham Crown Court heard her renewed application this morning in the most high profile case to be televised since cameras were allowed into the Court of Appeal for the first time last month.
Shaun Smith QC, representing Philpott, said she will forever be known as a 'child killer'. But he said there has been a 'clamour for the draconian punishment' even before she was sentenced, and she should have received a lesser sentence due to her husband Mick's influence over her.
He said: "Whatever happens from now on, there will be a number of permanent reminders of her inability to say stop."
He added: "Her time in custody will inevitably carry with it the risks attached to all inmates serving sentences involving the death of children.
"When she is released she will have no support network, nobody supports her, at all.
"She will never again be allowed to have children or be involved with children."
But the appeal was rejected and there was applause in court as the verdict was read out, and a call of 'you go back to prison and tell her that' was heard from the public gallery.
Philpott, 33, and family friend Paul Mosley, 46, got 17 years for the manslaughter of the children in a house fire in Derby in May 2012. Mick, 56, has not appealed, and a plan for Mosley to appeal has been abandoned.
Jade Philpott, 10, and her brothers, Duwayne, 13, John, nine, Jack, eight, Jesse, six, and Jayden, five, all died in their bedrooms after a fire swept through the family home on Victory Road in the Allenton area of the city.