Dunne, who sprang to prominence after sharing the 54-hole lead in the 2015 Open at St Andrews as an amateur, began the week 118th in the Race to Dubai, with only the top 117 on Sunday earning full playing privileges for next season.
The 26-year-old was just 0.7 points behind Jack Singh Brar in the standings, but while Singh Brar enjoyed a share of ninth place at halfway, Dunne could only add a 74 to his opening 71.
Birdies on the second and third had Dunne in position to avoid a 12th missed cut in 14 events, but a bogey on the ninth was followed by a disastrous triple-bogey eight on the 12th after driving out of bounds.
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England’s Lee Slattery, who came into the event in 115th place on the money list, also looks set to lose his card after missing the cut following rounds of 72 and 75.
At the top of the leaderboard, England’s Oliver Fisher holds a one-shot lead on the course where he carded the first 59 in European Tour history last year.
Fisher fired two eagles and four birdies in a second consecutive 65 to finish 12 under par, with South Africa’s Justin Walters and South Korea’s Jeunghun Wang, who are 121st and 119th on the money list respectively, on 11 under.
“I played really well the first two rounds last week, my driving was a lot better in France and I just got on a couple of bad runs around that course, which we all know can happen,” Fisher said.
Dunne’s early exit was good news for Singh Brar, who added a bogey-free 68 to his opening 67 to lie five shots off the lead.
“It’s been quite tough the last couple of weeks. I thought just have fun out there and what will be will be,” said the 22-year-old, who is coached by former European Tour player Anthony Wall.
“He (Wall) has helped me quite a lot the last few months, on the mental side mostly. I felt like my game’s been quite good but I just haven’t quite pushed on well enough.
“I played really nicely, probably left a couple out there coming in but I’m pretty happy. I’m just going to stay aggressive and keep trying to make birdies.”