What is the ruling on one who suffers from continuous abdominal pain and constant flatulence at the time of Fajr prayer, which compels him to repeat ablution multiple times and makes it difficult for him to perform the prayer on time?

If the emission of wind is continuous such that it does not cease for a period allowing you to perform ablution and prayer before the prayer time expires, then you fall under the ruling of one afflicted with incontinence (sahib al-salas). In this case, you must perform a single ablution after the prayer time begins, and then offer the prayer within its prescribed time. What is emitted thereafter will not harm you, even if it occurs during the prayer itself, and your ablution will not be nullified by it. Rather, you continue your prayer until you complete it, as a facilitation and removal of hardship.