It sounds like your car wasn't too badly contaminated to begin with, which is why you're only getting a bit of gunk showing up on/in the clay after working the horizontal surfaces and almost nothing on the vertical surfaces. Logically, fallout is going to be prominent on those horizontal surfaces because it's falling down, not sideways.

From what you describe, with regular kneading of the clay, you should be able to use that clay for many more cleanings. I've seen cases where one bar of clay was still "good" after claying half a dozen vehicles and others where one bar alone wasn't enough to do a single vehicle. It all depends on how heavy the bonded contaminants are.

Meguiar's is now selling a clay replacement pack - 3 bars of 50g each for about $19.