Li was champion on red clay at Roland Garros in 2011 and on the hard courts of the Australian Open in January but grass has proved to be tougher surface to conquer for the popular Chinese player.
Her hopes of improving on three previous quarter-final appearances ended on Friday when she whipped a forehand long on match point to become the highest seed to fall so far at this year's championships.
Zahlavova Strycova raised her arms in triumph as she finally reached the second week of a grand slam at her 33rd attempt and after more than a decade of trying.
The 28-year-old will play former world number one Caroline Wozniacki for a place in the quarter-finals.
(Writing by Pritha Sarkar; editing by Clare Lovell)
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