Madsen won his first European Tour title in the South African Open on Sunday and shared the lead with defending champion Charl Schwartzel at the start of the day.
However, the 25-year-old Dane three-putted the first for a bogey and then dropped another shot on the par-five second, hitting a straightforward chip across the green and into a bunker.
At six under par, Madsen was three off the lead now shared by his playing partner Schwartzel and former Ryder Cup player Soren Hansen, with Schwartzel having birdied the second and Hansen picking up shots at the second and third.
They enjoyed a two-shot lead over the chasing pack, with Portugal's Ricardo Santos, France's Victor Riu and English duo Richard Finch and Ross Fisher all on seven under par.
Finch, who had been 10 under par and three clear during his second round only to finish bogey, bogey, double-bogey, had birdied the first, while Fisher had birdied the second but then missed from two feet for par on the next.
Spain's Carlos Del Moral, recent winner of the European Tour's qualifying school, had set the clubhouse target on six under after a 66.