Do I have a dead nipple? Left looks saggy and doesn't get hard as often as the right. (photo)

Thank you for sharing your question and photograph.  For being four weeks out from surgery your left nipple appears alive and well.  The nerve sensation to the nipple has likely been affected from either the surgical procedure itself or from the swelling present in your tissues.  This will hopefully resolve spontaneously given enough time, i.e. 6 months or more, so allow your results more time to mature. Hope this helps

I am going to assume that by "dead", you mean that it's numb. This isn't unusual. As your swelling continues to subside, the sensation should return. Best of luck.

When a plastic surgeon hears "dead", I think of tissue not surviving. In your case, the nipple/areola complex is alive and well. It sounds like you may have aesthetic concerns and/or change of sensation.  Best to follow up with your plastic surgeon for accurate assessment and advice. Best wishes.

It will take several weeks or even months for the return of normal sensation.  The body has an amazing ability to repair itself; hence, the injured nerves repair themselves gradually as the patient moves forward to his recovery, a process referred to as reinnervation. 

Good luck and best wishes.