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Robinson was the defending champion, but could not get to the top of the podium yesterday.
Robinson attacked the hard, icy course with her trademark aggressive skiing on the first run.
She got hung up on her inside ski a couple of times, resulting in some minor errors which cost her precious time.
She was 2.33sec behind leader Marta Bassino of Italy after the opening run.
Run two was similar for Robinson, with small mistakes costing her valuable time. She finished the race 3.93sec behind Bassino, who won ahead of Tessa Worley, of France and Michelle Gisin of Switzerland.
Fellow NZ skier Piera Hudson also lined up but failed to finish her first run.
"I had a good start to my race but unfortunately hyper-extended my knee coming off the first pitch and have sprained my lateral ligament.
Fortunately, it doesn't seem too bad so we'll asses it again in the morning and see if I can race again," she said.
Another giant slalom was set to go ahead at the same field last night.