The most common cause of nipple necrosis (death) after any surgery would be poor blood flow. This would be an unusual complication, but smoking, hypertension and obesity will increase your risk for this complication.
Nipples rely on blood flow from surrounding tissues. During breast surgery that separates the nipple from some of those sources of blood flow, the nipple may not maintain enough healthy blood flow to survive. This is a very rare complication of breast lift and breast augmentation, as most of the tissue underneath the nipple is left intact. Smoking dramatically increases the rate of this complication, as nicotine constricts the important small blood vessels extending to the nipple.