if you say: "for YOUR health" you have to translate: alla TUA salute" or even "per la TUA salute"
No native speaker would ever say Fa bene alla tua salute.
Salute belongs to the group of nouns that do not usually take a possessive adjective, unless wishing to clearly emphasise the owner (should this be required for some special reason).
In order to indicate the owner without any emphasis, as in this sentence, an indirect object clitic pronoun is used before the verb:
Fa bene alla salute. = It is good for (anybody's) health.
Ti fa bene alla salute. = It is good for your health.