It's our understanding that ClickBank's affiliate system is cookie-based, so there's nothing about our button or system that would delete the cookie set in the buyer's browser when they click a CB affiliate's link, which should get detected by CB during checkout.
Basically, our button just adds an extra layer to the process going from the affiliate's link to checkout, about the same as if the buyer looked at an additional page on your site before they actually proceeded to checkout.
The affiliate may need to clear cookies from their browser first, to start testing with a "clean slate", then they can click their own affiliate link to reach your site and click your Buy Now button to proceed to ClickBank checkout, and then they should see their CB affiliate ID credited for the sale. It may even be possible that affiliate doesn't have a proper CB affiliate referral link, so it's not setting their affiliate cookie to begin with.