Is the statement that one does not need to repeat ablution after its third invalidation correct, and what should one do in the case of repeated invalidation of ablution by wind during prayer and recitation of the Quran?

If ablution is definitively broken during prayer, one must repeat ablution and the prayer, based on the Prophet's (peace be upon him) saying: "If one of you passes wind during prayer, let him leave and perform ablution and repeat the prayer," and his saying: "The prayer of one of you is not accepted if he passes wind until he performs ablution."

However, if the impurity is continuous, one must perform ablution for each prayer after the time for it has begun. It is permissible to perform prayers, supererogatory prayers, and recite the Quran from the Mus'haf or by heart. What is discharged during that time does not matter, in accordance with Allah's saying: (So fear Allah as much as you are able), and the hadith of the woman with continuous non-menstrual bleeding: "Then perform ablution for every prayer."

As for reciting the Quran by heart, it is permissible without purity, except for someone in a state of major ritual impurity (janabah). Touching the Mus'haf is not permissible except with purity from both minor and major ritual impurities.