I realize this is probably a necro-post but after reading the manual I found a section referring to Wired Connection operation. At the very bottom of the section it states "When connected with a source device via a connecting cord... and playback has been stopped for about 20 minutes, the system turns off automatically."
My solution was to turn the source device volume all the way up and then use the SRS-BTM8 to control the actual volume. This fixed my problem. My theory is the audio in jack has a volume threshold while sensing playback. If the volume on the source device is too low, then it assumes playback has stopped. Hopefully this helps someone.