I guess I should have said "Sometimes scaling down doesn't work well". But even if everything else is equal, making it smaller is automatically going to make the cg range smaller, too. Additional factors can add to that but if you make a 50% smaller plane, that is identical in every way to it's big brother, the only difference being that it is half the size, you have essentially given it more drag to contend with due the relative size of the air molecules it "sees". The smaller version is going to be flying in essentially a denser fluid than the larger (yes, air is a fluid). Also, if big brother has a comfortable CG range of a 10 or 20mm, little bro is down to 5mm or 10mm so you can see how it can get out of hand very quickly. And this doesn't even take into account materials thickness and mass distribution, which unless you can find a half size foamboard, IS going to be different.
Now, these are reasons why it is harder to scale down, but the center of lift on the plane and it's relationship with the center of gravity and where the CG needs to be doesn't change with scale.
Sorry, I didn't mean to ramble on. Aerodynamics is one of those things that just isn't easy to explain, even when you keep it simple...