According to Reuters, a court ruling in the city of Peja said: "British citizen Andrew Charles Kingston Soper should not be extradited because offences he has been charged with exceeded the statute of limitations."
Andrew Soper, also known as Laurence Soper, was a Catholic monk alleged to have abused children during his time teaching at St Benedict's School in Ealing, West London, between 1972 and 1984.
He left the UK when his ministry came to an end and has never been charged with any crimes.
The British government summoned him for further questioning in 2011 however he did not return, prompting a European Arrest Warrant to be issued for him.
He was found five years later in the Kosovan city of Peja where British authorities requested for him to be extradited back to Britain.
Kosovan courts refused, saying Mr Soper's crimes were too long ago, prompting British authorities to appeal.
The Crown Prosecution Service said at the time: "We are pleased that the prosecutor in Kosovo has lodged an appeal against the judge's decision in this case.
"The CPS and other agencies continue to do all we can to ensure this individual is extradited following a request by the UK government."
However on Monday a court in Peja turned down the British government appeal, marking their second refusal to extradite Mr Soper.
Premier has contacted the Crown Prosecution Service for a response.
