Ailsa Craig, which lies 10 miles off Girvan in the Firth of Clyde, is back on the market for £1,500,000.
The 245-acre volcanic plug, the source of the granite used for Olympic gold medal-winning curling stones, is home to colonies of protected birds.
However, those rare selling points have not been enough to persuade anyone to part with the original asking price of £2.5m.
It was put up for sale in 2011 by owner Charles Kennedy, the eighth Marquess of Ailsa, but has failed to find a buyer.
Known as Paddy's Milestone, the Craig is home to 70,000 birds, including gannets, guillemots, razorbills, kittiwakes and herring gulls, and is managed as an RSPB Nature Reserve.
Any new owner would be able to command a rent of about £26,000 a year.
The RSPB, which has managed the island for more than 25 years, said previously it was not in position to buy the island.
Dr Dave Beaumont, RSPB Scotland regional reserves manager, said: "Our lease on the island runs until 2050.
"We will be watching the sale closely and will be very keen to work with the new owners to further the conservation of this magnificent island."
Ailsa Craig is about two miles wide and rises 1100ft above the sea.
The firm that makes curling stones has a lease to extract 'blue hone' granite from a quarry on the island.
It was from there the curling stones used by the gold medal winning Scottish Women's Curling Team at 2002 Winter Olympics were made.
There are also three cottages, a ruined castle and a lighthouse on the island. It is being sold by Vladi Private Islands, which has sold more than 2000 islands worldwide since it was set up more than 30 years ago.
A spokesman for the firm said: "The island is still on the market and not sold as of yet."