Britain's Harriet Dart lost to Australian world number 47 Ajla Tomljanovic in the last 16 of the Nature Valley Open in Nottingham.
Dart, ranked 159th in the world, lost 6-7 (5-7) 6-1 6-2 in her second grass-court match of the season.
The 22-year-old was broken twice in the opening set but won the tie-break before losing the second and third.
She failed to convert four break points, including two at 2-2 in the deciding set.
On Wednesday British number three Heather Watson lost 6-4 6-3 to Greece's Maria Sakkari, ranked 82 places higher, in the first round in rainy conditions.
Compatriot Katie Swan also lost to American Bernarda Pera 7-6 (7-5) 6-1.