The former Sunday school teacher was jailed for a minimum of 18 years in 2011 for murdering Mr Buchanan and her ex-lover's wife Lesley Howell.
Their bodies were found in Castlerock, County Londonderry, in 1991, and police thought they had killed themselves.
Stewart, 52, was jailed for plotting the murders with Colin Howell.
Howell, a former dentist, pleaded guilty to the murders in 2010 and is serving a minimum of 21 years in prison.
Stewart's appeal in 2013 against her conviction for the murder of Mrs Howell was dismissed.
At that stage, she dropped a challenge against her conviction for the murder of Mr Buchanan, her first husband.
But her lawyers sought permission to relaunch that appeal.
They said the abandonment should be annulled because she was allegedly not advised by previous legal representatives that it would amount to a dismissal.
But a judge in Belfast said the fresh grounds for appeal were "without foundation".
He said Stewart, who appeared via prison video-link, had fully accepted the advice of previous counsel that an appeal against the conviction for Mr Buchanan's murder was groundless.
"She knew that the quest was finished," he added.
The court also rejected claims that the trial judge failed to properly warn the jury to look for more than just accomplice evidence from Howell of Stewart's guilt.
The judge said her application had to be refused.
Stewart's lawyers are continuing with separate attempts to have the Criminal Cases Review Commission refer her conviction for killing Mrs Howell back to the Court of Appeal.
Double killer Hazel Stewart has lost an appeal against her conviction for the murder of her husband Trevor Buchanan.