Michael Ross was 15 when he shot Shamsuddin Mahmood, 26, in the head in Kirkwall's Mumataz Restaurant.
The former Black Watch sniper was jailed for a minimum of 25 years in 2008 after being convicted of murder.
Ross has been told by the Scottish Criminal Cases Review Commission there is not enough evidence to support a miscarriage of justice claim.
Mr Mahmood was shot in full view of a room full of diners, including families with children, by a masked gunman.
A man jailed for the murder of a waiter in Orkney in 1994 has failed in a bid to have his conviction re-examined.