Se me va la voz

Se me va la voz
 

I saw this song title today, but it has confused me. I know it means something like "losing my voice" but I don't quite understand how. Specifically, how does the "se" and "me" work? Is this the reflexive version of "ir", so that "se" and "ir" go together to mean "to leave", and "me" is there just to tell that is it my voice that is leaving? If that's true, why isn't it "me se va la voz"? What's the rule for which pronoun comes first in this case?

You're right, irse is the verb being used, and it can be translated as 'to leave'.
Pronouns go before the conjugated verb in a specific order. The reflexive pronoun is the left-most pronoun. Object pronouns are placed closer to the verb.
The direct object pronoun, if any, is closest to the verb.
The indirect object pronoun, if any, is to the left of the direct object pronoun.

In Spanish, it's very common to get 'impersonal' about things. You don't drop something; it drops from you. This same kind of idea is in play here. The person is not losing her voice; it is leaving her.