Balu, who lost to Amrita Mukhejee, was cruising in the second round contest as she didn't let her rival win a single game in the opening set but eventually she ran out of steam and lost 6-0 4-6 2-6.
Amrita will now clash with top seed Prarthana Thombare, who fought off the challenge from Damini Sharma 6-7 (4) 6-3 6-0 in her second round match at the Sania Mirza Tennis Academy, which is hosting an ITF tournament for the first time.
Third seed Natasha downed Sharon Sanchana Paul 6-1 6-4 while seventh seed Eetee blasted past Rishika Ravindran 6-0 6-2.
In the bottom-half of the draw, second seed Shweta Rana defeated Arthi Munian 6-2 6-3 to set her last-eight stage contest against sixth seed Nidhi Chilumula, who blanked wild card D Venugopal Tatachar 6-0 6-0.
The final quarter-final will be between fourth seed Rishika Sunkara and eighth seed Bhuvana Kalva.
Rishika outplayed Reshma Ganapathy 6-0 6-1, while Bhuvana faced stiff resistance from Manya Nagpal before prevailing 6-4 7-5.