Unfortunately a lot of people on here don't know how to use the clutch on a G25/G27 because it is banned for most events one here (yes I know its more realistic and harder to drive with, and has been a part of Prologue since day 1, but it gives an advantage, similar how using a using a wheel gives an advantage over someone with a controller- that all has to be taken up with the management...)
I have been using it for over 2 years with Prologue and what I have found is, the more the RPMs have to change for the gear change you are attempting, the more time you need the clutch in and gas off. Since the 1-2 shift usually has the biggest change in RPM's, it needs more time to prevent getting neutral. That's why it works for you when you do it very slowly.
As an example if you tried to go from 1st to 3rd, you would find you really need to have the clutch in a long time to prevent neutral as that would require an even large RPM drop. Also, this implies that for cars where the RPM's drop fast, they can be shifted faster and you will less likely to get neutral. Again this is all based on my experience.
After some time you will probably get used to doing the 1-2 shift slower, it just takes a bit of practice.
Also, as you may have found, if the wheels are spinning when you try to shift, you will need to do a slower shift to prevent neutral. This is very unrealistic, and more of a bug in my view. In a real car the wheels simply will stop spinning the instant the clutch is depressed or you go to full lift, but not in so in GT.