I know this problem might be similar to the issue that causes the Prime App to crash the BT box, but it is somewhat different. The app doesn't crash, the video stream plays but all buttons on the controller become ineffective. The only way I can regain control is to power cycle the box.
In addition the Prime app is horrendously slow to start and load video streams (although BBC iPlayer, Netflix, etc. are pretty slow to load) when it does load the sound plays several seconds before the picture appears.