Bopanna and Dodig, seeded 13th, lost 7-6(4) 4-6 6-7(3) to fourth seeds Rajeev Ram and Joe Salisbury in the third round.
Sania Mirza will be in action at the Cincinnati Masters, pairing up with Tunisia's Ons Jabeur in the women's doubles.
AITA also released its complete correspondence with the International Tennis Federation (ITF) concerning the qualification of India's men doubles team for the Tokyo Olympics.
Following being accused of not qualifying for Olympics on merit, Bopanna shared an alleged phone call with AITA general secretary Anil Dhupar, where the official said qualification is possible.
Bopanna accused AITA of misleading everyone by claiming it had changed the combination by pairing him with Sumit Nagal for a shot at qualification.
The International Tennis Federation (ITF) communicated to the AITA that Nagal was eligible for men's singles, hours before the deadline for entries expires.
The contest resumed with the 14th seed pair of Jean Julien-Roger and Andreja Klepac having a one-set lead and they finished on the right side of the result with a 6-3 3-6 11-9 scoreline.
Also rules out the country's presence in the mixed team competition, it's best chance for a podium finish.
Bopanna and Shapovalov will take on German duo of Alexander Zverev and Tim Puetz in the quarter-finals.
Rohan Bopanna and Aisam-ul-Haq Qureshi, the duo which was given the title of 'Indo-Pak Express', will team up after seven years in the upcoming Mexico Open tournament.
Bopanna and his Chinese partner Yingying Duan lost 4-6 4-6 to the pair of American Bethanie Mattek-Sands and United Kingdom's Jamie Murray in a first-round match that lasted an hour and three minutes.
Rohan Bopanna and Ben McLachlan lose opening round 4-6, 6-7 (0), to Ji Sung Nam and Min-Kyu Song.
Bopanna was on one of the three flights out of a total of 17 Tennis Australia-arranged chartered planes, that landed in Melbourne with positive cases on board.
India's Rohan Bopanna and Austrian Oliver Marach stunned ninth seeds Fabrice Martin and Jean-Julien Rojer in a hard-fought second-round encounter to enter the men's doubles quarterfinals of the Paris Masters.
Divij Sharan's and Rohan Bopanna's campaigns at the Astana Open ended following losses in the quarter-finals and Round of 16 respectively in Nur Sultan (Kazakhstan) on Thursday.
The unseeded Indo-Canadian pair fought hard before going down 6-4 5-7 7-10 to Chardy-Martin pair in the tie-breaker late on Friday.
The pair of Rohan Bopanna and Denis Shapovalov was knocked out in the quarterfinals of the 2020 US Open.