It is very usual. He wants to be understood.
In the beginning he gooed and babbled and you talked back, he thought you were communicating, then somewhere around 15 months (maybe closer to 12 or 18) he realized you don't know what he is saying. This often is a very trying, frustrating, tantruming age. And now (I would guess he is right around 2) that you are starting to understand what he is saying it is so reaffirming and exciting to hear you repeat his thoughts!
I think this usually lasts for maybe 6 or 8 months after they really get understood, but even at 3 or 4 it can sure help just to repeat their exact words. Then as they get older (like 6 or 7 and even friends or husbands
) it still is important to repeat what a person is saying, if you really want them to feel understood. Just by this time repeating their exact words is not near as reaffirming as putting it into your own words to show you are really listening and understanding.
So no, I don't think that the desire for someone to repeat what we say ever goes away it just evolves.