With touch-up paint, I think the main goal is to make it "better". It will never look like it did pre-chip.
You should be careful about how often you sand, though. As you said, you are not just sanding the chip, but rather all the surrounding paint. If you are sanding until you have to add more touchup, you are sanding it way too much. The problem is that as you level the touchup, you lower the regular paint.
How are you applying the touchup? You don't want to have a big blob of it there, you want it to be pretty flush already. Using a toothpick works well, and I've heard a match works great too.
Then, sand it to help level/smooth the blob, but you will never get it to all be perfectly flush, because you are sanding the touchup and the original paint. You need to polish it out after sanding, because sanding leaves a haze. What grit sanding block are you using, and how are you applying the Diamond Cut? If it were me, I'd use something like 3000 grit paper or block, spend a bit more time sanding (as 3000 grit is pretty slow), and then start with something like Dual Action Cleaner/Polish to remove the sanding marks. Then step up to the next level if this isn't strong enough to remove the marks.
To fix what you've already done, it might be better to try polishing with a lighter polish to see how it ends up, and then I guess take it from there. Hopefully you don't need to add anymore paint or do anymore sanding, you just need a milder polish to restore a smooth finish to the paint. Sorry this is kind of rambly, it's not exactly clear what state your paint is currently in...
