In Nusach ashkenaz, as well as in "V'hi Noam" of Nusach haAri, the last pasuk of "Yoshev B'seter Elyon" (Psalm 91) is repeated.
Why is that?
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Machzor Vitri - page 114 says we say the verse Orech Yamim twice in order to complete the name of Hashem that is produced by doing so. וכופלין אורך ימים כדי להשלים השם היוצא ממנו
Tashbatz 258, Maharam says we say it twice this way it has the numerical value of Kohanim, since the Chashmonoim when they went to war said 7 times Vyehi Noam and twice Orech Yamim and were victorious.
Avudraham says it is a protection of the 248 Aivorim.
A late answer, I know, but a different one (and, I must say that I still don't understand some of the claims made in the other answer so this one is as reasonable, but I can't find a source for it).
The Birnbaum siddur Hasiddur Hashalem writes (page 310):
ארך ימים is repeated so that the number of verses of this psalm reach a total of seventeen, the numerical value of טוב
Though, based on some of the answers to my question, one wonders if the repetition isn't because of the "completion of a section" -- we have just had 2 sequential psalms (90 and 91), (at least) 3 psalms in a row with a particular theme (being saved/protected/given shelter from threats via closeness to God) and are about to begin 2 other sequential psalms which shift the theme and are litanies of praise. Just a thought.