The man, in his 60s, had been diving the 65m-deep WW2 wreck Pinto, which lies some 17 miles out from Fanad Head in Donegal.
He was last seen on an 18m decompression stage by other members of his group, according to the Irish Coast Guard.
Emergency services were alerted at around 4pm on Saturday, 12 August, when he failed to resurface.
A Coast Guard rescue helicopter from Sligo and the Lough Swilly RNLI lifeboat searched for the man until 10.30 that night, resuming at first light on Saturday and continuing throughout the day. They were assisted by the Portrush lifeboat and a number of local dive- and fishing-boats.
Sea conditions were described as heavy and challenging, with 5m swells on the Saturday, but on Sunday two teams from a dive-boat were reported to have been able to carry out searches in the vicinity of the wreck.
The dive group had been using a charter-boat that had set out from the village of Downings in Sheephaven Bay.
Their objective, the Pinto, was a convoy rescue ship torpedoed by U-482 in September 1944. It had been attempting to pick up survivors from the tanker Empire Heritage, sunk earlier by the same U-boat.
Divernet – The Biggest Online Resource for Scuba Divers