I have an 07 klx 250 with just under 600 miles. I am breaking it in as per Kawasaki instructions. I also changed oil at 100 and 500 miles with Silkolene Comp 4 Semi-Synthetic.
I have had missed shifts between 1-2 gears during the first 500 miles. I thought it was because I was keeping under 4000 rpm and was "shifting early". Now that I am revving out to 6000 rpm., the other day after riding about 1/2 hour I could not get it into 2nd gear. I only had 1st and neutral.
I limped home in 1st gear and shut it off. After an hour I started it and it worked great. Today I took it to work and it shifted smoothly. What gives? The dealer said bring it back when it doesn't work again.

 

Try holding the shifter level up for one more second while shifting.

Sometimes my KLX will do the same when fully warmed. Just gotta give it more love on 1st to 2nd. Any gear after, I can go all out.

 

Don't slam it into first or second. Lower RPMs helps too.

I've got about 2600 miles on mine and frequently have a hard time going from 2nd to 1st, less the other direction but I miss 2nd on the upshift occasionally too.

The type of oil you use can make this better or worse too.

 

I'll tryholding up the shift levertomorrow. I thought it may be oil related.Many years ago someone told me toadd STP in my Harley trans., the trans was seperate from the engine. It wouldn't shift at all till I drained the STP.
Thanks

 

it might just be the shift star. there is a whole write up in here about it(with pic's) i was having the exact same problems your experiencing. i did the shift star mod and haven't had a problem since. it's a fairly easy mod.