Australia's Ajla Tomljanovic will have all night to ponder what might have been before resuming her clash with eighth seed Aryna Sabalenka in the Netherlands.
The world No.71 took the first set 6-3 over the Belarusian but narrowly surrendered the second in a tiebreak 7-6 (7-5) when rain stopped play.
The last-16 match will resume on Friday morning at 0-0 in the deciding set.
Other affected matches include the clash between Germany's Antonia Lottner and Elise Mertens of Belgium, who were tied at 2-2 in the opening set at the time.
The weather also caused the postponement of Dutch third seed Kiki Bertens' match with Kirsten Flipkens of Belgium, but America's Alison Riske had enough time to defeat Fanny Stollar of Hungary 7-6 6-2.
Riske will face top seed and compatriot CoCo Vandeweghe in the quarter-finals on Friday with seventh seed Aleksandra Krunic of Serbia also due to face Russia's Veronika Kudermetova.
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