Just wanted to put this in but I have my screensaver set to turn on after 10 minutes with no activity and watching Plex Live TV and not touching the remote for 10 minutes quits the app and the firestick screensaver shows.
The workaround is set the screensaver to larger span of time before it triggers on the device but just wanted to make a note of it.
Watching Top Gear if that helps anything
