After looking at your code, what's most likely happening is that because the next link isn't quite being set properly, it is interfering with how the API key is provided. This would in turn cause the API respond with a 403 error because it does not recognize the API key.
The best way to resolve this is to make a minor adjustment to how you're implementing the pagination. The correct method would be to assign params as follows:
$params = array('next' => $results->next);
If you're still having trouble after making this change, please let me know!
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