What happens to a product that is no longer available on Amazon?

This product gets "Disabled" status and is no longer available in the catalog (frontend). In case if certain option is enabled. By default this option is enabled.

Disable Missing Products option - Amazon Products Manager Extension

This is a step-by-step guide on how to filter Amazon products using Amazon Magento plugin.

This useful Magento extension allows you to easily find and import Amazon products into Magento.