Does Sauron come back to life?

Answer 1

No. He lives as the Eye of Sauron and can also see through the rings made in Mordor and control the black riders. Some could say he is dead since he has no body, but, since he's an evil wizard, and only has his mind and magic left, he's still alive. Unfortunately.

When the One Ring is destroyed, Sauron did perish.

Answer 2

Sauron is not a mortal creature and it is not accurate to say he lives or can die. In ages past, he created the One Ring, a magical focus for his mind control powers. He invested so much of his power into the ring, that he became fully dependent on it, meaning when it was cut from his hand by Isildur, he was weakened so much that he lost his physical form.

It took many years for him to gather his power back, enough for him to reappear, to summon his servant Nazgul, and to raise an army. However once the One Ring was destroyed, once again he was weakened so much that his physical form was lost. This time there was no return, he would never be able to regain his strength, he would remain forever banished.