Here are two relevant passages from their EULA/TOS. The TL;DR: download your content to avoid getting fucked.
e. Availability of Purchased Digital Content . Purchased Digital Content will generally continue to be available to you for download or streaming from the Service, as applicable, but may become unavailable due to potential content provider licensing restrictions and for other reasons, and Amazon will not be liable to you if Purchased Digital Content becomes unavailable for further download or streaming. You may download and store your own copy of Purchased Digital Content on a Compatible Device authorized for such download so that you can view that Purchased Digital Content if it becomes unavailable for further download or streaming from the Service.
f. Downloading and Risk of Loss. If you plan to download Digital Content that you purchase or rent, we encourage you to do so promptly after your purchase or rental. If you are unable to complete a download after having reviewed our online help resources, please contact Amazon customer service. Once you purchase or rent Digital Content and we make the Digital Content available to you, you are responsible for completing the download, if you choose to download, and for all risk of loss of the Digital Content after download.
e. Availability of Purchased Digital Content . Purchased Digital Content will generally continue to be available to you for download or streaming from the Service, as applicable, but may become unavailable due to potential content provider licensing restrictions and for other reasons, and Amazon will not be liable to you if Purchased Digital Content becomes unavailable for further download or streaming. You may download and store your own copy of Purchased Digital Content on a Compatible Device authorized for such download so that you can view that Purchased Digital Content if it becomes unavailable for further download or streaming from the Service.
f. Downloading and Risk of Loss. If you plan to download Digital Content that you purchase or rent, we encourage you to do so promptly after your purchase or rental. If you are unable to complete a download after having reviewed our online help resources, please contact Amazon customer service. Once you purchase or rent Digital Content and we make the Digital Content available to you, you are responsible for completing the download, if you choose to download, and for all risk of loss of the Digital Content after download.
source: http://www.amazon.com/gp/help/customer/display.html?nodeId=2...