Jason Day has battled and scrambled his way around Royal Liverpool with considerable grit and determination to keep himself in the hunt for another major triumph at the British Open.

But like the rest of the Hoylake field, Queensland's former world number one, looking to add to his 2015 PGA triumph, appears as if he's scrapping for second place as US leader Brian Harman enters the final round five shots clear.

On an afternoon when champion Cameron Smith effectively conceded his chances of back-to-back wins was over and Min Woo Lee's challenge faded despite a late charge, it's all down to a rejuvenated 'J Day' to bring the Claret Jug back to Australia.

But despite a third-round two-under 69, Day is seven shots behind in a tie for fourth.

It all looked very promising early on as the 35-year-old from Beaudesert birdied three of his first five holes, holing from 10 metres at the fifth to offset a careless bogey at the third.

And when he found more inspiration at the ninth, missing the green but then putting up from the fringe to hole from 7.5m, the birdie elevated him into joint-second.

But gritty perspiration rather than inspiration was largely the order of the day as Day made six gutsy up-and-downs to maintain momentum.

But he couldn't grind it out without a mishap and, having missed the green at the 14th, he putted up from a greenside swale too softly and the ball rolled all the way back to him, 15m away.

He kept grinding away but was the picture of frustration when he fractionally missed another lengthy birdie putt at the final hole.

Clearly so frustrated with his efforts despite being only two behind second-placed Cameron Young, Day declined all his post-round interviews, even with host broadcasters Sky.

After Thursday's opening round, he'd done the same, sweeping off to the range straight away to work on his game.

Lee, who'd started the day at three under alongside Day in a tie for fourth, failed to launch a challenge at all, dropping three shots in his first six holes.

He eventually did hole for successive birdies at the 15th and 16th, from 2m and 3m respectively, to end at two under par, but was 10 shots adrift of Harman, tied for 17th.

He was cheered on around the course by his double-major-winning sister Minjee Lee, but even she couldn't inspire him.

"I saw her a couple times. Yeah, it was good to have her out here," said Lee.

"I feel like I'm out of the question (of catching Harman), so I've got to shoot a really, really low score tomorrow, and that's doable."

Smith's chances of firing himself into final-round contention also evaporated.