The defending champion could only manage an even par 72 on Saturday following her 67 on day one, slipping into a tie for 5th at five under.
With a bogey on the 2nd and a birdie on the 15th, Ko was steady on her 18th birthday to finish four strokes behind the leader Brooke Henderson of Canada.
Henderson, a tour rookie four months younger than Ko, has risen to the lead from 9th place after carding the day's low round of 65.
Meanwhile, after the 2nd round of the China Open in Shanghai, Aucklander Michael Hendry dropped from a share of the lead into a tie for 13th after carding a one over par 73.
Hendry is at three under par, five strokes behind the leader Julien Quesne of France.
The New Zealander Ryan Fox has missed the cut after rounds of 73 and 77.
In New Orleans, at the latest event on the PGA tour, the Manawatu's Tim Wilkinson carded a second round 69 before bad weather stopped play.
Rotorua's Danny Lee was four under through 10 holes on day two to be level with Wilkinson at six under par.
Both players are five strokes behind the clubhouse leader Hudson Swafford of the United States.
Swafford's compatriot Boo Weekly is also at 11 under with three holes left to play in his second round.