Jonty Evans and Cooley Rorkes Drift AKA 'Art' were competing at Tattersalls International Horse Trials on 3 June in the CIC3* when he fell at the main water feature on the cross-country course.
A statement released by Eventing Ireland this week said,
"Jonty remains in a stable but serious condition in Hospital.
"Jonty has now been moved from intensive care at the Beaumont Hospital to a high dependency ward in the Connolly Hospital, Blanchardstown, West Dublin.
"Unfortunately, there is no change to report in his condition from the most recent update. Jonty remains unconscious, with a very serious head injury.
"The family deeply appreciate all the care for Jonty from the Beaumont Hospital staff and the support and messages from all his family and friends.
"Further updates will be issued if there is a change in Jonty's condition."
Horse Sport Ireland had already confirmed that the 46-year-old suffered a "significant brain injury" after falling from Cooley Rorkes Drift and that it “may take him many months to recover”.