This exact same thing happened to me. I just turned on my Roku one night and the Amazon Prime channel was missing. Then Amazon didn’t even come up on a search of channels to install. The thing is, it won’t show on a search because the Roku knows it’s already installed. The problem is just that the Home Screen on Roku somehow forgot that it was a shortcut so it doesn’t show it. I had to:
• restart my Roku by unplugging it for about 15 seconds.
• search for the location of the app on my Roku and uninstall it.
• reinstall the Amazon Prime app as a new channel, and then sign into Amazon and use their code from their site; something like “amazon.com/mytv”
Now it works again, and I can see the app on the Home Screen just like before (I had to move it up from the bottom of the list)..