Does the ablution of a woman afflicted with constant discharge become void upon the entry of another prayer time while she is performing the Fajr prayer, which she started at sunrise, and is she required to repeat the prayer?

One must not delay the prayer until its time becomes constricted. The person with urinary incontinence (sahib al-salas) is not obligated to repeat the prayer if the time for it expires while he is performing it. This opinion is strong, especially given the presence of hardship.