See, to repeat something thrice means you mean it seriously. It becomes an oath, you have to follow it/do it. A kind of promise
Why do all shanti mantras end by chanting 'shantih, shantih,shantih' three times? It means that the recitor earnestly hopes for peace.
Same here - when you say Namah Tassyai thrice, you are -what to say- taking an oath to fall at the Goddess, feet.