Often times, words are repeated in certain parts of the prayer so that the words fit well with the particular tune being chanted. Rabbi Yehuda Modena (Zikne Yehuda, § 131), Rabbi Moshe Feinstein (Igrot Moshe, vol. II, Orah Haim, § 22) and the Aruch HaShulhan (§ 58) all reference the Mishna (Berachot 5:3) when discussing this situation. The Mishna says that if during the prayer one says “Modim, Modim” rather than just “Modim”, one should be silenced since it appears that one is praying to two deities. That being said, if the words being repeated do not give the appearance of praying to two deities, then it would seem that it would be permissible.
There is no clear proof among the Poskim as to whether repeating words is forbidden or permitted, but many say that it should be avoided if possible. Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 7, § 39) says that it is preferable to use tunes which do not require repeating words, but that if there are tunes which have been chanted for generations which involve repeating words, then there is room to be lenient. Rabbi Moshe Feinstein (ibid.) says that if by repeating words the meaning of what is being chanted changes then it should be avoided. For the most part, repeating words does not alter the meaning of the prayer and therefore, if necessary, one may do so. An example of this is “Levanon, Levanon Vesirion” when Mizmor LeDavid is chanted in Kabbalat Shabbat. In such a case there is no appearance of praying to two deities and the repetition of the word Levanon does not change the meaning of that particular verse.
Summary: There is room to be lenient when repeating words in a prayer when a particular tune necessitates it.