Divij Sharan and his Serbian partner Nikola Cacic fought hard before going down in three sets
Experienced Indian Rohan Bopanna and his Canadian partner Denis Shapovalo advanced to the second round of the US Open men's doubles event after a straight-set win in New York.
But for the 23-year-old Bouchard, a former world number five who has slumped to 56th in the rankings, it was another blow after her first-round exit in Indian Wells.
In an interview last month after a World Tennis Tour event at the Greenbrier in West Virginia, they said they had not yet decided whether they were finished competing. Playing almost exclusively with each other throughout their 25-year careers, the Bryans captured a professional era record 119 titles, including 16 Grand Slam wins, 39 ATP Masters 1000s and the ATP Finals title four times.
There will be no Indian presence in the singles main draw at the Australia Open this year with Yuki Bhambri stumbling at the final hurdle, losing his third and final qualifying round match to Ernesto Escobedo, in Melbourne on Saturday.
Fourteen-time Grand Slam champion Rafael Nadal has entered the quarter-finals of the ATP Acapulco tournament with a comprehensive straight-sets victory over Italy's Paolo Lorenzi.
Defending champions Leander Paes and Radek Stepanek had to work hard to cross the first round hurdle in the men's doubles even as Sania Mirza advanced in both the mixed and doubles events at the US Open.
Images from all the action on Day 4 of the Australian Open in Melbourne on Thursday
The year's final grand slam began with an upset as 13th-seeded Frenchman Richard Gasquet was upended 6-2 6-2 6-3 by Britain's world number 84 Kyle Edmund at the U.S. Open on Monday. Gasquet, who has reached the last 16 at Flushing Meadows four times in his career, was outplayed throughout and his U.S. Open experience lasted just one hour, 41 minutes.
Asian Champion Amit Kumar assured India of at least a silver by storming into the finals of the 55kg category, on the opening day of World Wrestling Championships in Budapest on Monday.
World Championship silver medallist wrestler Amit Kumar rued that a bad umpiring decision at the end of his bout cost him a deserving gold medal in the final of the 55kg category against Iran's Hassan Farman Rahimi.
American qualifier Sachia Vickery completed an astonishing comeback to stun third seed Garbine Muguruza 2-6, 7-5, 6-1 in a second-round win at the BNP Paribas Open in California on Friday.
Eugenie Bouchard's mid-season nosedive continued on Tuesday as the Canadian was swept aside 6-3 6-4 by Croatian qualifier Donna Vekic despite having home advantage and the backing of an excited crowd in a first round clash at the Rogers Cup.
World number one Simona Halep swatted aside American Nicole Gibbs while Maria Sharapova was flawless in her straight sets victory over Romania's Mihaela Buzarnescu in the opening round of the Shenzhen Open on Monday.