Is it permissible for one who suffers from continuous flatulence or incontinence to perform ablution and prayer, given that the emission of gas or the sensation of its emission continues after relieving oneself and performing istinja (cleansing), which prolongs the period of purity and makes it difficult to perform prayers in public places?

Repelling wind does not affect the validity of the prayer. If wind is emitted continuously in an uncontrollable manner, then the person is afflicted with chronic flatulence ( سلس الريح). In this case, the afflicted person performs ablution for each prayer after its time has entered, and prays the obligatory and supererogatory prayers without interrupting the prayer due to the emission of wind. Istinja’ (cleansing) from it is not legislated. It is recommended to repel whispers (waswasah) and to take the matter with ease.