The St Leonards cueman was edged out 5-4 by Rod Lawler in an epic four-hour quarter-final battle at the German Masters on Friday night.
The opening six frames were shared. World number 14 Davis - who reached the first three ranking event semi-finals of his career last season - won the second, third and sixth, the latter thanks to a break of 63.
Lawler edged in front again by claiming the seventh and was a ball away from clinching victory in the eighth only for Davis to clear the colours and pinch it by two points.
A run of 44 gave Davis the advantage in the decider until 50th-ranked Lawler replied with a 44 of his own. It was nip-and-tuck moving onto the colours, but Lawler potted brown, blue and pink to reach his first ranking event semi-final since the 1996 International Open.
Earlier the same day Davis achieved a good 5-2 win over 23rd-ranked Chinese potter Liang Wenbo in the last 16. Davis led 3-1 at the interval with top breaks of 88 and 57, and runs of 55 and 51 made it 4-1. Wenbo pulled one back thanks to an 89, but Davis finished it off with a 71.
The previous evening Davis saw off former world champion Graeme Dott 5-1. Davis took the first four frames via breaks of 70, 78 and 63, and although 16th-ranked Dott stayed alive through an 87, a 66 in frame six sent Davis through.
Reigning six-reds world champion Davis, who beat David Gilbert 5-3 in round one on Wednesday afternoon, will be back at the table on Friday morning in European Tour event eight.