Bhupathi and his Australian partner Jarmila Gajdosova frittered away early advantage to lose 6-4 6-7 (7) (8-10) to Chinese Taipei's Hao-Ching Chan and Brit Jamie Murray in a contest which lasted one hour and 40 minutes.
The Indo-Australian pair made a strong start, breaking its rivals once, to clinch the opening set in 29 minutes, saving four break points in the process.
But Chan and Murray bounced back in the second set, one of the five break points they earned to stretch the set into a tie-breaker and eventually draw level.
In the junior competition, Pranjala Yadlapalli defeated South African Katie Poluta 6-4 6-3 to enter the girls' singles competition.
Among the boys, Sumit Nagal defeated American Michael Mmoh 6-2 4-6 6-4.
However, in another girls' singles match, Ojasvinee Singh let slip an opening set advantage to lose 6-0 4-6 1-6 to American Olivia Hauger.