I had this exact same problem and the information available on the internet is surprisingly sparse for this issue, despite it being fairly common. Strangely, it was a thread for the Millenia where I found the clues to the source of the problem.
The issue is, apparently, the head unit, at some point starts to fail to send a low amp signal to the Bose Relay under the hood...and once this signal fails to be sent, the relay never switches, and the Bose amp never powers on. The strange thing is, this failure can be intermittent as mine was. I went three weeks with no audio, then all of the sudden it started working again. This is how I knew for sure that A) no fuses were blown and B) my amp wasn't toast.
Under the hood, you can remove the not-broken relay for the Bose system and place a paperclip on the two silver contacts, completing the circuit to power your amp. If your issue is the same as mine you'll have sound as soon as you turn your stereo on. I suppose it's possible you just have a bad relay, but I swapped mine with a neighboring good relay, and nothing changed.
I haven't yet implemented a permanent work-around for this failure of the head unit's, but there are definitely many ways to work around this. I haven't decided yet which way I want to go. I currently have a 10 amp fuse jammed into the silver contacts, meaning my amp is technically always on
But I have sound back!!