the fact that you have the latest software on a recent model of ipod is probably the exact cause of the issue. apple in their infinite wisdom are continously moving the goalposts in the sense that the so called universal ipod and iphone connector is far from universal.
what i am saying in a nutshell is that the bose dock will have been programmed to understand information from all known apple devices at the time of manufacture, but cannot be guaranteed to work with newer variations. essentially your ipod speaks a different language that the dock doesn't understand.
it would be worth 'rolling back' the software updates to check. if the ipod works when returned to the previous software then you know that is the problem. if not, then i suggest either the dock connector on the ipod or on the bose is faulty. presumably your usb cable and charger etc still work so it's more likely the bose.
believe me i sell ipod docks among other things so i know what i'm talking about. and this is one of the reasons i don't use an ipod, or bose products ;)