Help & troubleshooting for channels on your Roku device, including adding/removing channels, logging in to, authenticating, or activating a channel, channel-specific playback issues, assistance contacting channel publishers to report issues, and adjusting channel-specific settings.
If it only happens with Prime, and other channels stream without issue, then the problem appears to be with Prime itself. It's very likely that whatever server you are getting the stream from is having issues maintaining the stream. Either Amazon is having a hardware issue at their end, or there's something wrong with the channel/app on the Roku player. Roku themselves are not who is responsible for the channel, that would be Amazon.
Usually, the first thing to try is to remove the channel from your Roku, reboot the Roku (must do or the removal isn't completed), and reinstall the channel. Sometimes the channel just gets a hiccup, and a reinstall clears it. But if that doesn't resolve the problem, then it's time to contact Amazon for help. Since it isn't happening with other channels, it's not the Roku itself or your Internet connection.
That said, I will say that I had a problem with Netflix several years ago, and the problem was traced to some 3rd party on the Internet that was throttling my Netflix. It was outside my ISP's control, and eventually it went away. But it was annoying.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.