What year is it? How many miles are on it?
The R6 has a sloppy tranny, if you have to pull up abnormally hard, then you might want to check the linkage. Look at the swivel points on each end, and make sure that they do swivel. If one is stuck, than it does effect the shifting. I took my shift linkage off---for something---oh yeah, to drop a tooth, and when I put it back on, I put lock-tight on the screw that holds it in place, and some accidentally got into the swivel, and froze it up. I could have sworn I had tranny problems, because down shifting was REALLY hard. So for a little troubleshooting, I took it back off to check the swivel again, and noticed it was frozen. WD-40, and 30 minutes of messing with later, I put it back on and it was perfect.
If it has a lot of miles on it, or if you...slap-shift it hard in 1st-to-2nd gear wheelies, there might be worn dogs on 2nd gear, making it not want to go into 2nd very easily, so it just goes with neutral instead. That, or a bent shift fork.
So, linkage, bad dogs, or a bent fork...those are what you have to choose from as to what the problem is.
