I have two guesses, the first would be that you have your activity set up to leave unused devices turned on. My second guess would be that you have the remote set up to send the stop command when you leave the watch a blu ray activity. Both of these options should be under the more options tab or something like that for your watch a blu ray activity.
If you want you can send me a private message with your Harmony login info and I can log in and check you settings. I have done this for many people here. If you are worried about me having your password you can set it to something temporary like 12345 and then set it back after I check your settings.