Columba McVeigh, one of 16 murder victims known as the Disappeared, was kidnapped on 1 November 1975.
His body has never been found, despite extensive searches.
His sister, Dympna Kerr, said this anniversary was "particularly painful".
His brother, Oliver, said: "Is 40 years not long enough to punish a family?"
Mr McVeigh added: "Someone has the information that can end this inhumanity at absolutely no risk to themselves.
"It is all about the information - we just need a little bit more."
Four searches for the County Tyrone man have been carried out at Bragan Bog in County Monaghan in the Republic of Ireland.
The most recent was in 2013, when a specialist forensic team spent five months on excavation work.
The Independent Commission for the Location of Victims Remains was set up by the British and Irish governments in 1999 in an effort to gain confidential information about the location of the bodies of the Disappeared.
The commission said it had no plans for further searches in relation to Mr McVeigh at this stage, but stressed the importance of fresh information coming forward.
Frank Murray, one of the commissioners, said: "The fact that we have yet to find Columba does not mean that this is a lost cause - far from it."
He said that while a "huge expanse" of Bragan Bog had been searched, what they now needed was more information "to refine the search area".
"That's what happened in the search for Brendan Megraw, whose remains were found last October, some 15 years after searching commenced," he said.
"I can give an absolute guarantee to anyone who has information and brings it to the commission that it will be treated in complete confidence."
Mrs Kerr said if her brother had lived he would have celebrated his 60th birthday last September.
"Not only was that denied us but we have nowhere to gather to mourn him," she said.
"All we can do is pray that someday we'll get him back and plead with anyone who has information to help bring an end to this nightmare."
Sandra McPeake, of the WAVE Trauma Centre support charity, said: "Someone who can help bring an end to [the family's] intolerable suffering should search their conscience to do what is right."
The family of a man murdered and secretly buried by the IRA has made a fresh appeal for information on the location of his remains on the eve of the 40th anniversary of his disappearance.