It's not always an obvious question to some and isn't meant to be condescending but, is your internet connection fast enough to support a 1080p stream?
When you're using Internet Explorer as your web browser you'll need an up to date version of Silverlight installed.
Otherwise, make sure you're using the most up to date version of each browser.
Finally, Amazon states that for HD support to work, your system must conform to and have HDCP enabled, otherwise they will provide you the SD version as a fall back.
The easiest way I know of to check the HDCP status of your configuration is to download and run
Cyberlink's Ultra HD Blu-ray Adviser tool that checks for Blu-ray playback compatibility. It works for BR, BR3D, and UltraHD. It tells you the details of what is and isn't ready in your system for those tasks, but the key for your situation is, it will tell you your HDCP status.