The SoundLink Mini 2 isn't really intended for this use, but the setup you describe should work. The Speaker does have a power-save mode, but it will generally only enter this when no audio is detected. The most likely explanation here is that the speaker is getting a very weak signal from the TV and boosting it enormously with its internal amp. (this would require you to turn the volume on the SLM 2 up very high.)
If you are using a headphone jack or similar on the TV, try increasing the TV's output level while turning the speaker's volume down. This should provide a stronger signal on the AUX port which would prevent the speaker from sleeping automatically.
Hope this helps!
Also having the same issue when using it with my PC. I have the volume turned all the way up on my computer and yet the device still mutes itself.
Not impressed Bose.
New to the Bose family as far as soundlink goes. My AUX cord is plugged into my lapptop and charges as needed on base station. I have tried the reset, multiple AUX cords and an update and all still fail to keep music playing more than a couple of minutes. When I use bluetooth off of my phone it does just fine. I have it on my desk just a couple of feet away from me so it is easy enough to unplug the aux and plug it back in and voila the sound starts playing again....but I really should not have to do this...ALL DAY!!!
What is the solution? The Mini is about 2.5 months old and past the time I am able to take it back to Best Buy.