Molik, who has missed the last eight weeks on the WTA tour with an ear infection, failed to impose herself against an opponent ranked 100th in the world.
Fifth seed Tatiana Golovin of France remains on course for a semi-final meeting with top seed and defending champion Maria Sharapova after coming through her second round match unscathed.
The Moscow-born 17-year-old, who lost in last year's Edgbaston final to Wimbledon champion Sharapova, beat South African qualifier Natalie Grandin 6-4, 7-5.
Sharapova will face Australian 16th seed Samantha Stosur in the third round on Thursday after Stosur overcame compatriot Evie Dominikovic 6-1, 1-6, 7-6.
Japanese sixth seed Shinobu Asagoe won her second round match against Meilen Tu of the U.S. 6-1, 4-6, 6-1. Compatriot Ai Sugiyama, the eighth seed, beat Australia's Nicole Pratt 7-5, 6-4.
