In September, Robert Howard was granted leave to seek a judicial review of the coroner's decision to examine the 1994 disappearance of Arlene Arkinson.
His legal team claimed the move was an attempt to undermine the not guilty verdict returned against him in 2005.
The body of Arlene, who was 15, has never been found.
Howard's lawyers argued that the inquest is being used as a way of reopening issues surrounding the case because the Arkinson family were unhappy with the outcome of the criminal trial.
On Monday, a High Court judge confirmed he had dismissed Howard's application for a judicial review.
Mr Justice Treacy said he would issue a judgment setting out the reasons for his decision on Wednesday.
Life sentence
Arlene, from Castlederg, County Tyrone, vanished after attending a disco in Bundoran, County Donegal.
Howard, 67, who formerly lived near her home, was charged with her murder but acquitted at trial.
The jury did not know that by then he was already serving life for raping and killing 14-year-old Hanna Williams from Deptford, south London.
Her body was found in a cement works in Northfleet, Kent, in March 2002.
Howard's lawyers, who unsuccessfully tried to have reporting restrictions imposed on their judicial review application, pointed out that the coroner's stated purpose was to allow Arlene's death to be registered.
It was argued that this could be achieved through an alternative, High Court procedure with the Presumption of Death Act 2009 coming into effect.
A convicted child killer and rapist has lost his legal challenge to the holding of an inquest into the death of a schoolgirl he was cleared of murdering.