Paula Parfitt, 41, of Strood Kent wants doctors to keep treating Pippa Knight and had taken her case to the Court of Appeal.
But three appeal judges have ruled against her.
Ms Parfitt thinks Pippa should leave hospital and wants specialists to stage a home-care trial.
Doctors treating Pippa, who is in a vegetative state at the Evelina Children’s Hospital in London, disagree and say life-support treatment should end.
A High Court judge earlier this year ruled against Ms Parfitt.
Mr Justice Poole decided treatment could lawfully end and said Pippa should be allowed to die.
In February, Ms Parfitt asked appeal judges to overturn Mr Justice Poole’s decision.
Lady Justice King, Lord Justice Baker and Lady Justice Elisabeth Laing delivered a ruling on Friday and upheld Mr Justice Poole’s decision.
Lord Justice Baker said in a written ruling: “I am entirely satisfied that the judge was entitled to conclude and declare that it was lawful and in Pippa’s best interests that life-sustaining treatment be withdrawn for the reasons he gave in his judgment.”
The other two appeal judges said they agreed.
Campaign group the Society for the Protection of Unborn Children has paid for lawyers to represent Ms Parfitt.
John Deighan, deputy chief executive of the society, said after the ruling: “This is a desperately sad day and a decision which allows despair to triumph over hope.”
He added: “This courageous young girl has fought to live with every breath in her body for the last two years but the court has decided that fight has been in vain.”