With the new translation of the Roman Missal, we're getting back a feature that had been hidden away in the Latin for 50 years: the threefold "mea culpa." That puts the Confiteor back on the list of liturgical triple plays, along with the Kyrie (Lord have mercy), the Gloria ("you take away the sin of the world, have mercy on us"), the Sanctus (Holy, Holy, Holy) and the Agnus Dei (Lamb of God). As it is, only the "mea culpa" was trimmed down in the first translation of the Order of Mass.
Repetition is one of the features of the Latin that formed the liturgy's way of expressing faith. It's a form of emphasis, or a kind of superlative. The repetition may not be strict: we don't say "Lord have mercy. Lord have mercy. Lord have mercy" but "Lord have mercy. Christ have mercy. Lord have mercy" (Trinitarian! The first "Lord" is addressed to the Father, and the last to the Spirit.) Repetition also takes the form of parallel phrasing. Look at the Gloria:
"You take away the sins of the world, have mercy on us;
you take away the sins of the world, receive our prayer;
you are seated at the right hand of the Father, receive our prayer."
But wait, there's more!
The repeated invocations in the Mass often build up to a kind of crescendo. That happens first with the mea culpa:
mea maxima culpa ."
It's in the Gloria ("you are seated at the right hand of the Father"), and the Agnus Dei, too:
"Lamb of God, you take away the sins of the world, have mercy on us.
Lamb of God, you take away the sins of the world, have mercy on us.
Lamb of God, you take away the sins of the world, grant us peace."
Actually, the only time our "triple play" doesn't advance to a crescendo is in the Sanctus, when we are quoting from Isaiah's vision of heaven!
I guess if something is worth saying once, it's worth saying three times: not for God to get the point, but for the point to get to us.