https://www.youtube.com/watch?v=gmGc5gQT2ok The video explains my issue fairly well. I'm having trouble with why the second one, which is exactly the same as the first one, doesn't work.

I THINK what happens is (on the second one), after the first button press, the dropper on the bottom feeds the item back into the top dropper, but the top dropper somehow receives a redstone input and drops the item back into the hoppers in front of it, which feeds back into the bottom dropper. Then, on each subsequent button press, the cycle repeats itself. Is the signal still active during that time? If so, why doesn't it do the same for the first one?

Or maybe the item gets pushed through the top dropper and drops back into the hopper?