Sloane Stephens' Nuremberg Cup hopes were in the balance against Yulia Putintseva when play was suspended on Tuesday.
Stephens, the world number nine, is the top seed, but she did not have it all her own way in the opening two sets of her first-round clash.
The US Open champion edged the first 7-5 but was pegged back 6-4 in the second, with Putintseva holding her own at 3-3 in the third when poor light halted play.
Sixth seed Sorana Cirstea and Mona Barthel progressed into the last 16, with the latter facing reigning champion Kiki Bertens next, while Kristyna Pliskova booked her place in the quarter-finals.
Pliskova defeated second seed Julia Goerges in the first round and followed that up with a 6-3 7-5 victory against Lara Arruabarrena on Tuesday to set up a meeting with Johanna Larsson, who beat Christina McHale 6-3 6-0.
At the Internationaux de Strasbourg, two seeds progressed and two were knocked out on a day of only four matches.
Mihaela Buzarnescu and Dominika Cibulkova made it through to the quarter-finals, but Danielle Collins and Timea Babos went down to Qiang Wang and Zarina Diyas.