The underlying mechanism is basically the same, so maybe there´s simply some dirt inside or it´s been heavily.

I had an iPod with a bad center click, it turned out the pirce of rubber connecting the actual mechanism with the center button cover was misaligned and wasn't making good contact with the button. Fixing this requires opening the iPod, however.

Do you happen to have an aftermarket face plate by chance, the click wheels those come with are inferior.

I’ve changed both faceplate, click wheel and center button. It’s the same as it was before.