Jelena Dokic was one of them, the number four seed finishing her rain-affected first-round clash with Paula Ormaechea but losing it 4-6 6-3 6-4.
In the other last-32 meeting carried over, top seed Marina Erakovic cruised through, beating Stefanie Voegele 6-3 6-4.
Following Dokic home was third seed Romina Oprandi and the number-seven-ranked Lourdes Dominguez Lino.
Oprandi was beaten in straight sets, 7-6 (7/5) 6-4 by Timea Babos, while Lino lost to Mariana Duque-Marino 4-6 6-2 7-5.
Elsewhere, there were wins for Lara Arruabarrena-Vecino, 6-4 6-0 against Eva Birnerova, and Yaroslava Shvedova, 6-2 6-2 against Valeria Savinykh.