I assume you're referring to the Siri remote for Apple TV version 4. If so, I believe that it turns off the Bluetooth radio when sleeping. When you wake it up, probably by moving it (remember, it has a motion sensor), it reconnects and ATV reports "Remote connected". If that message is your problem, you might have made it clearer in your title and description. Since you're immersed in the movie, I assume you're not using the remote to control the system. If you leave it alone, it should sleep happily. If you're using it to adjust volume, maybe you could use another remote for that.
By the way, your profile (sig) says Apple TV 2, iOS 9.2.1, which doesn't make sense. You should correct it, maybe to Apple TV 4, tvOS 9.2.1.