Published Thursday, 17 May 2012
Search teams will leave the site next week. (© Pacemaker)
Mr McVeigh, from Donaghmore in Co Tyrone, was 17 years old when he was abducted and murdered by the IRA in October 1975.
Fresh digs began at Bragan Bog earlier this year after new information was passed on to the Independent Commission For The Location Of Victims' Remains (ICLVR).
However the ICLVR teams are now preparing to leave the site.
"The work programme at Bragan is now drawing to a conclusion," said a statement from the ICLVR, released on Thursday.
"We have not been successful in locating the remains of Columba McVeigh."
Previous digs have taken place on nearby bogland just across the Irish border for the teenager, but to avail.
The latest search saw hundreds of mature trees on the bog were cut down to open the site up for excavation and allow forensic archaeologists to inspect roots.
Investigators leading the searches for Northern Ireland's so-called Disappeared have appealed for anyone with new information to come forward.
"All searches undertaken by the ICLVR are information led and we would appeal for anyone who has information on this or any other disappeared cases to contact the Commission," the statement continued.
"All information will be treated in the strictest confidence and it cannot be used for any purpose other than locating the remains of victims.
"Confidential free-phone number: 00-800-55585500."
© UTV News