The concern about repetition in prayer is common; this is good, because it shows that people are paying attention to Jesus' words & how to apply them. I would just like to offer another piece of Scripture, some food for thought when we're discussing the possibility of repetition being unbiblical. Try to see how the use of repetition enhances this passage, and how vain repetition could be different:
Psalm 136, RSV
O give thanks to the Lord, for he is good,
for his steadfast love endures for ever.
2 O give thanks to the God of gods,
for his steadfast love endures for ever.
3 O give thanks to the Lord of lords,
for his steadfast love endures for ever;
4 to him who alone does great wonders,
for his steadfast love endures for ever;
5 to him who by understanding made the heavens,
for his steadfast love endures for ever;
6 to him who spread out the earth upon the waters,
for his steadfast love endures for ever;
7 to him who made the great lights,
for his steadfast love endures for ever;
8 the sun to rule over the day,
for his steadfast love endures for ever;
9 the moon and stars to rule over the night,
for his steadfast love endures for ever;
10 to him who smote the first-born of Egypt,
for his steadfast love endures for ever;
11 and brought Israel out from among them,
for his steadfast love endures for ever;
12 with a strong hand and an outstretched arm,
for his steadfast love endures for ever;
13 to him who divided the Red Sea in sunder,
for his steadfast love endures for ever;
14 and made Israel pass through the midst of it,
for his steadfast love endures for ever;
15 but overthrew Pharaoh and his host in the Red Sea,
for his steadfast love endures for ever;
16 to him who led his people through the wilderness,
for his steadfast love endures for ever;
17 to him who smote great kings,
for his steadfast love endures for ever;
18 and slew famous kings,
for his steadfast love endures for ever;
19 Sihon, king of the Amorites,
for his steadfast love endures for ever;
20 and Og, king of Bashan,
for his steadfast love endures for ever;
21 and gave their land as a heritage,
for his steadfast love endures for ever;
22 a heritage to Israel his servant,
for his steadfast love endures for ever.
23 It is he who remembered us in our low estate,
for his steadfast love endures for ever;
24 and rescued us from our foes,
for his steadfast love endures for ever;
25 he who gives food to all flesh,
for his steadfast love endures for ever.
26 O give thanks to the God of heaven,
for his steadfast love endures for ever."
And as long as it's the subtlely beautiful Jesus prayer in question, bringing up a prayer from Jesus Himself seems good:
"So, leaving them again, he went away and prayed for the third time, saying the same words." --Matthew 26:44
May God continue to bless us all!