Technically, he didn't need a horcrux or anything similar. As a Maia he's immortal - he is unable to die as long as Illuvatar wants him to exist. Only Illuvatar can destroy one of the Ainur. Thus the never ending resurrections - Sauron dies what, five, six times in the whole history (Silmarillion and LOTR both)?
Only three or four times, if we get technical. Plus, Sauron wasn't one of the Ainur, and it wasn't Illuvitar who finally destroyed him completely. On another note, Sauron was able to ressurect himself so many times because of how powerful he'd become, almost as powerful as Morgoth. His will was strong enough for his spirit to endure until only the ring remained, the last link tethering him to the world.
I will admit that I get a lot of things mixed up and how he wasn't one of the Ainur? He WAS a Maia - and both Maiar and Valar were Ainur, right?
What you wrote kind of collides with what I remember. Research time.