Does this passage forbid praying for the same thing repeatedly?
It does not.
Both Paul and the Lord himself demonstrate that recurring prayers making request for the same thing — even using the same words — and even prayers uttered at length are entirely appropriate (cf. 2 Cor. 12.8; Mk. 14.39; Lk. 6.12).
The original text reads as follows:
“And, while praying, you should never babble idly like the Gentiles do, for they suppose that, by their garrulousness, they shall be listened to.”
The Gentiles did not view their deities as creatures interested in aiding mankind; instead, they were selfish beings, reluctantly aiding humanity only when it amused them. Hence, idolaters were inclined to nag and harass their false-gods into action. It is to these methods of praying that the Lord refers.
The term, “garrulousness,” literally denotes: many-words. And the term, “babble idly,” has to do with uttering mechanically repeated phrases — blubbering useless repetitions.
The Gentiles frequently chanted the same words over and over, sometimes for hours (cf. Acts 19.34). In effect, they were filibustering their deities, until, becoming fatigued by the badgering, their gods finally gave in to humanity’s requests.
By contrast, the true God is willing to give, and generous in his giving, for he is interested in aiding humanity (cf. Jms. 1.5; Heb. 2.16-18). He does not need to be nagged with repeated chants until he gives in to the petitioner, for he acts for our benefit even when we ourselves do not know what we need (cf. Rm. 8.26; Mt. 6.8).
Take note of these points and pray accordingly.