Britain's Katie Swan in action against Tamira Paszek
Image credit: Imago
Swan shocked Kristina Kucova, ranked 748 places higher than her, 6-3 6-4 in the first round but could not repeat the feat on Wednesday.
Compatriot Dan Evans did fair better though, after a surprise 6-4 0-6 7-5 win against eighth seed Matthias Bachinger.
Evans has slumped to 752nd in the world rankings but is now just one win away from a fourth appearance at Wimbledon.
Three Australians are closing in on the Wimbledon men's singles draw too after securing wins on Wednesday.
Former Wimbledon boys' champion Luke Saville, along with John Millman and John-Patrick Smith each edged to within one win of a coveted berth in the main draw.
Saville beat 20th seed Thiemo de Bakker 6-4 6-4, Millman defeated Frenchman Tristan Lamasine 4-6 6-1 6-4 and Smith overcame American Bjorn Fratangelo 7-6 (7-5) 6-4.
Geraint Thomas (Stage 11, 2018)