Flipkens, of Belgium, needed three sets to put away Ukrainian Lesia Tsurenko 7-5, 3-6, 6-3. Defending champion Arvidsson, of Sweden, fell to New Zealand's Marina Erakovic 6-1, 3-6, 6-3 -- with Erakovic getting retribution for a loss to Arvidsson in last year's Memphis final.
Third-seeded German Sabine Lisicki reached the quarterfinals with a 7-6 (7-0), 4-6, 6-2 win over Hungarian Melinda Czink Wednesday.
Britain's Heather Watson, seeded fourth, moved on with a 2-6, 6-0, 6-3 defeat of Czech Andrea Hlavackova, and No. 8 Kristina Mladenovic of France triumphed over American wild card Victoria Duval 6-1, 3-6, 6-3.
Stefanie Voegele of Switzerland gained the quarters with a 3-6, 7-6 (7-2), 6-1 decision over French qualifier Claire Feuerstein.