A judge on Friday concluded that a pregnancy termination was in the woman’s best interests.
Mrs Justice Lieven had analysed evidence at a hearing in the Court of Protection, where issues relating to people who lack the mental capacity to make decisions are considered, in London.
Lord Justice McCombe, Lady Justice King and Lord Justice Peter Jackson had considered the challenge at a Court of Appeal hearing in London.
They said they would give reasons for their decision at a later date.
Lawyers said they thought the circumstances of the case were unique.