Copyright is not like trademark. Amazon can choose to enforce it selectively, and it should not influence any specific case.
What would be a better option (IMO) then just not enforcing your rights would be to get an nominal fee from the entities you like and in return grant them a favourable license.
(Not a lawyer, go ask your own lawyer if you want specific legal advice)
For an example, lets just say for the sake of argument Amazon did decide to defend their API from Oracle's implementation and take action. Oracle could use as a defence (But prob not their only line of defense) that "That Internet Archive, LeoFS, Riak CS, Minio, cloudian and others all have S3-Like API's. Amazon must be aware that these products exist and by allowing such products to exist without defending their rights (what ever they are) to the API they allowed an implied license for the API to be created thus Oracle's implementation is just another implementation of that implied license.
A "Workaround" to such could be taking lets say Internet Archive to one side and saying "Hey, we like what you do, but we have a copyright on that API you are using. Pay us $1 and we will grant you a license to use that API.".
Personally I dislike the idea of enforcing copyrights on an API (Sure, enforce them code behind that API, unless you wish to give that away) and feel that the products using them should stand on their own.
Implied license generally applies to situations where a reasonable person would believe they have a license even though one has not been explicitly granted. For example, if I pay you for the use of a photograph you took, even without a written contract granting me ownership or a license, a court would hold that I have an implied license.
Failing to defend IP can enable a laches defense, but that's quite different from an implied license.
Off the top of my head (Which may not be a great example but the first one that sprung to mind) Field v. Google.
> The Field court expanded the earlier doctrine to hold that implied license arises "where the copyright holder knows of the use and encourages it." Applying this two-pronged knowledge and encouragement test to the Field facts, the court found that the website owner was aware of the robots exclusion protocol mechanisms for communicating with the Googlebot, and that by not using them, he essentially encouraged the Googlebot to index his content.
> Field created a robots.txt file for his site and set the permissions within this file to allow all robots to visit and index all of the pages on the site. [...] Field created the robots.txt file because he wanted search engines to visit his site and include the site within their search results.
and (regarding meta-tags):
> Field concedes he was aware of these industry standard mechanisms, and knew that the presence of a “no archive” meta-tag on the pages of his Web site would have informed Google not to display “Cached” links to his pages. Despite this knowledge, Field chose not to include the no-archive meta-tag on the pages of his site. He did so, knowing that Google would interpret the absence of the meta-tag as permission to allow access to the pages via “Cached” links. Thus, with knowledge of how Google would use the copyrighted works he placed on those pages, and with knowledge that he could prevent such use, Field instead made a conscious decision to permit it. His conduct is reasonably interpreted as the grant of a license to Google for that use.
Field was trying to get his site indexed and cached (so that he could sue Google), and Google indexed and cached it. The court ruled that Field's actions were active encouragement and implied the grant of a license to do the thing he wanted Google to do.
Field didn't fail to defend his copyright. He put the files up in January, filed copyrights with the Copyright office, waited for them to be indexed and cached, and sued Google in April. He protected his copyright about as vigorously as you can with the available legal tools.
The question of implied license in this case is whether putting something on the internet without taking steps to stop search engines from indexing+caching it constitutes an implied license. The court ruled it did, but it relied in part on Field taking specific actions to allow it (such as the robots.txt file), so it's not entirely clear that in a different case they would rule the same way. If someone put up a site with just a plain text file without HTML tags and no robots.txt file maybe the court would rule that there was not an implied license there, I don't know. They also took into consideration that there are well-known industry standard ways of preventing Google and others from indexing and caching your site, so maybe they would consider that alone sufficient to rule that there's an implied license if you don't follow the industry standards.
In any case, Field v. Google has little-to-nothing to do with failing to defend a copyright.