A new hearing was ordered "for further consideration," the Times of London said Thursday.
John Hogan, 34, appealed the ruling because, he contended, he was "not in control of his actions" and insane at the time of the incident in August 2006.
Two judges agreed, pointing out that Hogan's mental state "was simply not addressed" in the original session.
Hogan and his wife had gone to Crete for a vacation to attempt to save their marriage. Shortly before they returned home, Hogan allegedly pushed his son and his 3-year-old daughter off the five-story hotel balcony and then jumped.
The boy died, his sister and father survived.
Beautician charged with giving client fatal silicone butt injection
Duggar sisters unveil Christian dating rules in new book