I think I misunderstand Horcruxes here - are they used up? Or do they just exist to stop the person dying but are not actually 'used up' in the process? By this logic someone could be killed infinite times and still not die?
No, none were - they tether the soul to life.
Horcruxes work by keeping a part of the soul protected and earthbound, therefore tethering the soul to life, meaning the creator will not die even if the body is killed.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
They are not used up if their creator’s body is killed - none of the Dark Lord’s Horcruxes were used up when his body was killed at the Potter’s house. Therefore, yes, a wizard can become immortal and return infinite times from creating one Horcrux provided that Horcrux is not destroyed.