Ever since I got my Chromecast with Google TV I have not been able to use the Prime video app. I can load the app, i can browse through the shows but when i click watch video I get a message saying the HDMI is not connected. I have tried restarting the device, changing hdmi ports, deleting and reinstalling the app, checking for system and app updates with no luck. I have tried other devices in the hdmi ports and have had no issues. I have no issues using any other app on the chromecast either.
Thanks for reaching out and for doing some steps beforehand — these are of great help! Could you please try to clear the cache and data of the Amazon Prime app and check if the issue is also happening when casting via phone to your TV?
Also, if the issue is only happening with Amazon Prime, please reach out to the app developer for further help.