Is it necessary to repeat the prayer if the tissue used to guard against constant secretions disintegrated after the prayer, and its pieces scattered on the clothes, with uncertainty about the source of these pieces?

These discharges are the natural secretions of a woman's vagina. They are pure (tahir) but invalidate ablution (wudu'). Therefore, there is no need to guard against them or to purify clothes or the body if they come into contact with them. You are not required to place a tissue or to check after every prayer to avoid falling into whispers (waswasa). Any trace you see after prayer does not affect its validity, because "the origin of every new occurrence is estimated by the nearest time."