Yuki Bhambri, who has missed on-court action for five months this season due to injury, lost to Ireland's James McGee 7-5 2-6 5-7 in two hours and 19 minutes.
Sanam Singh also had a one-set advantage before eventually losing 7-5 6-7(3) 3-6 to Anderas Beck of Germany in two hours and 16 minutes.
The country's top player Somdev Devvarman, who has been struggling since the Delhi Open victory in February, had crashed out in the first round.
Sanam Singh committed nine double faults in the contest and Beck converted only three of the seven break chances. Beck broke Sanam four times.