I just disconnected my amp so we'll see what happens over the next couple of days.

Anyway, assuming that is why my battery keeps dying, what are my options? I don't feel like spending big bucks on a whole new Bose system from Infiniti, so hopefully just replacing the problematic component will be easy, but which component is at fault? The amp? The head unit?

 

Screw it get a double din kit and put and LCD in that thing. Problems=mods.

 

New HU, straight to the Bose speakers and get rid of the Bose amp? Or keep the amp (eg. the HU is the problem)?

 

your head unit is probably the culprit.

 

You can try to find a used unit from someone else to replace it with.