My 02 RM 125 does a similar thing. If its cold it will actually quit when going from neutral to 1st if you don't give it any gas. The problem lessens as the bike warms up. It's been like that since I got it 6 months ago but slightly worse now as the weather has been in the 40s and 50s. (By the way, my bike has a Hinson Clutch)
Myabe I'm taking the wrong approach, but my view is that if the clutch is working (i.e. I can slip it for starts and exiting corners), then I'm not that concerned about the problem you're describing.
By the way, in a previous thread, it appears that a lot of guys here are not using the clutch to shift after the start. My bike shifts smoothly without the clutch from 2-3 and on up, but using the clutch is like a timing mechanism for me and I can't seem to break myself of using it. I know there must be 5 shifts a lap where I don't use it though . . .
Rob