First of all, YAY for 1 cm! It feels good to know you have that much less to "do" when you go into labor, doesn't it?
I started losing my MP a few days after my first internal (I was 2 cm) and continued losing it throughout the week. I saw my last piece the day after my second internal (3 cm).
I've heard some women say they never lost it at all, or lost it during active labor.
But even if you never see it, you've still made good progress!