If the audio output level of your computer is very low low, or there are long periods of silence/inactivity on your VoIP interactions, The headset could be accidentally engaging it's normal auto shut-off. If there is an extended period of silence and there has been no interaction with the system by the user, the system will turn off automatically after 20 minutes.
If this is the cause of the problem, then either increasing the computer's volume or using the headset controls (volume +/-) every so often on the call should keep this from happening. Can you test to see if this symptom continues even with regular interaction to the on-board controls of the headset?
Thank you for the update! We're glad to hear that you are making progress on this and that your Bose product is not at fault in this case. Best of luck in resolving the remainder of this trouble!