Darren Clarke hit eight birdies on the third day of the Open to move up to six-under-par but said he felt he was too far behind for a title challenge.
Darren Clarke had eight birdies in his round of 67
But Graeme McDowell's hopes ended on the 17th when he thinned a bunker shot and ended on the road, leading to a quadruple bogey eight and round of 74.
Clarke had three bogeys in his round of 67 and three-putted on the final green.
"I am obviously too far back. It was another day of making too many mistakes," said Clarke.
"I played well again. I hit a lot of really good shots, hit it very close around the turn and made a lot of birdies but then made a couple of mistakes
"I gave myself lots of chances and unfortunately I have not shot the score I could have done."
England's Nick Faldo battled against a stomach upset as he carded a third-round 70 to reach three under for the championship.
Faldo started well, with birdies at the third and fifth, but parred the next seven holes before a bogey at 13 and a birdie at the last completed his day.
"I felt lousy as last night's dinner decided to go south," he said.
"I was not expecting 70 as I was on 50% power so I am really pleased. I was always going to battle on as it's the Open and I have time off afterwards."
Britons Ian Poulter and Simon Dyson also saw their Open chances slip away on Saturday when they fired rounds of one-under 71 and par 72 respectively to join Faldo on three under.
Dyson bogeyed the 10th and 11th, but birdied the second and 18th to end the day tied for 29th place.
Meanwhile, Poulter dropped shots at the opening two holes and at the 17th but birdied the third, fifth, 11th and the final 18th.
The 29-year-old's effort saw him join nine others, including Dyson and Faldo, in 29th.
Meanwhile, Luke Donald admitted partnering Jack Nicklaus as the legend made his exit from the Open on Friday had left him drained for Saturday's third round.
The out-of-sorts Briton fired a five- over 77 to drop out of contention, but he insisted he had no regrets.
"Being in among that much emotion is something I have not experienced but will never forget. It was a treat and will live with me forever," he said.
"But I felt low on energy today, lost concentration and I finished horribly."