Welcome to the Q&A Forum

Are you able to change the domain of buyproduct.com to shop.product.com and then have the shop's product pages and content which is duplicate have the same canonical? Not ideal as your shop would not feature any content.

If you are able to rework buyproduct.com then I would change the product page structure, enrich with hproduct data and other relevant markup (reviews).

I would do the following:

• For valid searches returned create a proper canoncial URL (and then decide if you want to do a index,follow or a noindex,follow on the result pages). You might not necessarily want to index search results, but rather a structure of items/pages on your site.
• I would generally not index search results (rather have your pages being crawled through category structures, sitemaps and RSS feeds)
• It does sound though that the way you implemented the search is wrong - it should not result in a soft 404 - it could be as easy as making the canonical for your search just "/search" (without any search terms) and if no results are found display options to the user for search refinements

The only time I have seen soft 404s with us is in cases where we removed product pages and then displayed a generic "product not available" page with some upselling options. In this case we set a status of 410 (GONE) which resolved the soft 404 issue.

The advantage of the 410 is that your application makes the decision that a page is gone, whereas a 404 could really be just a wrong linked URL.

If you only rolled it out to two of your retailers, I wouldn't think this is the reason for it. There could be various reasons for the drop of keywords such as new competition on paid ads. I would look at a competitive analysis of those keywords first.

In my mind, displaying a badge is no different to any legitimate affiliate scheme. I would perhaps evaluate the reputation of the domains linking to you and would perhaps also check your own domains reputation (via Google Safe browsing / WOT / Siteadvisor etc).

I doubt that you would notice a drop so quickly (especially if it was sudden and not gradual). To me it looks like competitors targeting the same keywords (via content or paid search).