It may be possible the shift drum detent arm may have an issue.
If you put the bike on a stand, when you shift gears manually, do you feel a positive gear selection? If not, then there may be a problem with the roller or spring on the detent arm.
If it feels like a solid positive gear change selection, then it may be the dogs or slots for 3rd gear are worn and slipping out of engagement, or a bent shift arm not allowing full engagement.
Worn dogs/slots or bent shift arms are fairly common on bikes that have seen a lot of "no-clutch" bang shifts.
Worn 2nd gear issues are fairly common on GSXRs.