The USPGA Championship, Whistling Straits, 12-15 August
Coverage: Live on Sky Sports, BBC Sport website, with updates on 5 live
Davies hits his tee shot at the second hole in his opening round
Rhys Davies finished the US PGA Championship at Whistling Straits four over par after a fourth-round 75 to total 292 for the event.
Davies had shot successive one-under-par 71s in his first two rounds to make the cut on the banks of Lake Michigan.
But the Welshman shot an eight on the par-four 18th after a bogey at the par-three 17th to ruin an otherwise good third round at the final major.
Davies posted three over par in Sunday's final round.
That saw him drop three places to joint 63rd while play was still underway.
Davies enjoyed a stunning start to his first full season on the European Tour, winning the Hassan II Championship in Morocco.
He had another three top-three finishes, but Davies' form has slipped recently and he missed the cut at the Open having finished a distant 74th at the US Open.
Davies is down to 17th on the European Ryder Cup qualification list and needed a big performance in the United States to maintain his hopes of appearing at Newport's Celtic Manor on 1 October.
There are nine automatic qualifying spots in European captain Colin Montgomerie's 12-man team, with three wild card places up for grabs.
Davies has been hailed as the "best putter in the world" by fellow countryman and Ryder Cup hero Phil Price, but the rookie has no realistic hope of a wild card spot.
The former Brynteg Comprehensive School pupil enjoyed an outstanding amateur career in college golf in the USA.
He combined his sport with a business degree at East Tennessee University, where local media called him "the best player to ever play" at the college.
In his final year there in 2007 Davies extended his own ETSU record for career individual titles to 10 and became the first UK player to reach number one in America since McDowell achieved the feat in 2002 while at Alabama State.