Caithness fired a second-round 70 for three under par and was four strokes behind Parker, who had six birdies in a flawless 66 to lead by two shots from English veteran Laura Davies and France's Virginie Lagoutte-Clement.
Caithness, with four birdies and a double-bogey at the eighth, shared sixth place with England's Trish Johnson (71), while Lynn Kenny was another Scot in the top ten after posting a 71.
Kylie Walker, the former Buchanan Castle amateur, made her first cut of her rookie season with a 71 for three over par and she was on the same mark as fellow Scot Pamela Feggans, who had a 73 to make the last round with a shot to spare.
A two-time winner already this season, Davies could have scored even lower after making four birdies in the first six holes yesterday. She dropped shots at the 11th and 17th and ended up with a 70.