Now Dr Stephen Lloyd, an art historian who has long insisted the painting was in fact done by an emigre artist, Henri-Pierre Danloux, has claimed X-ray evidence suggests it was not the work of Raeburn.
Dr Lloyd says the X-rays disclosed the painting lacks the lead-white paint Raeburn customarily used for his faces.
For good measure, his opinion is backed by Pierre Rosenburg, a former director of the Louvre and a prominent authority on French painting.
In a new book on Raeburn, which he has co-edited, Dr Lloyd says: "The X-rays show the lead-white paint which Raeburn commonly used to 'underpaint' his works shows up in the ice, landscape and sky of the painting but nowhere in the face."
He says X-rays of other works by the artist showing the use of lead-white paint add to a "compelling demonstration that this painting cannot be from the hand of Raeburn".
As long ago as March 2005, Dr Lloyd, then a senior curator at Edinburgh's Scottish National Portrait Gallery, told The Herald of his conviction that the Skating Minister – which dates from around 1795 and is said to depict Rev Robert Walker, minister of the Canongate Kirk and a member of the Edinburgh Skating Society, on Duddingston loch – was by Danloux.
Danloux was born in Paris in 1753 and emigrated to Britain in 1792 to escape the French Revolution.
The new disclosure is made in a book, Henry Raeburn: Context, Reception and Reputation, which Dr Lloyd has co-edited with Viccy Coltman, who heads Edinburgh University's history of art department. However, Duncan Thomson, former keeper of the Scottish National Portrait Gallery, reportedly said that Raeburn may simply have changed his technique at the time.
Sir John Leighton, director general of the National Galleries of Scotland, said: "There has been speculation for some time and no concrete evidence has yet been found to seriously undermine the traditional attribution to Raeburn."