I started the game last night and had to stop a few minutes in. I came back this morning...so 12 hours of inactivity. Obviously, the game lost its connection to the server when I went idle. I got a dialog as such and it started over with the Activision logo and the intro sequence. However, there was no audio whatsoever. I had to start another game on the Xbox and then restart Destiny to get the audio to come back.
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A simple workaround is to hit the home button the resume the game. It has worked for me everytime