I would recommend that you consult with your physician regarding your specific symptoms, but my understanding is that having an AN surgically removed does not affect your lifespan. I presume the exception could be if the AN caused damage to some of the critical structures near the brain stem, or other complications arose. I had an AN surgically removed and certainly plan to live a normal lifespan.
Regarding balance, one's balance will naturally deteriorate with age. I would expect this could be worsened in one that had an AN removed because the vestibular nerve on the AN side was cut. Vestibular exercises and/or tai chi can help. Have you tried these to see if they do? Something else could also be contributing to your imbalance, so it is best to consult with your physician.