Seventh seeded Bopanna and Dabrowski, the French Open winners, lost 6-4 3-6 8-10 to third seeded team of Hao-Ching Chan and Michael Venus.
In the men's doubles, Bopanna and Pablo Cuevas had lost to Simone Bolelli and the temperamental Fabio Fognini, who was later thrown out of the tournament for using abusive language against a woman chair umpire.
Leander Paes and Purav Raja have already lost in the second round of the men's doubles. Paes this year did not compete in the mixed doubles as Martina Hingis has paired with Jamie Murray. They are top seeded and have reached the quarterfinals.
Sania's challenge is still alive in the women's doubles, reaching quarterfinals with Chinese Shuai Peng.
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Meanwhile, in the girls singles, Mahak Jain lost 3-6 7-6 (5) 1-6 to Chinese sixth seed Xin Yu Wang while Mihika Yadav also went down in a three-setter.
Mihika lost 4-6 6-4 1-6 to American Nikki Redelijk. Zeel Desai was ousted by Colombian 12th seed Maria Camila Osorio Serrano 6-4 6-7(5) 6-3.
In the boys singles, Siddhant Banthia was thrashed 1-6 2-6 by American Danny Thomas.