Hi there,
Just like you I was having an issue with the Prime Video app stuttering at around 15mins on my Roku 3 after starting to watch a film, this also caused the audio to cut out, quitting the app, restarting my equipment etc. didn't fix the issue.
However as of last night (15/5) when I checked for any software updates, a new one for Prime video installed and I'm happy to report that I got through watching a couple of films without any further stuttering/audio issues.
Seems like it must have been a dodgy previous update, maybe they need to check this stuff before releasing it.
Hope this helps.