What is the ruling on sexual intercourse immediately followed by the onset of menstrual bleeding, given that the menstrual cycle is irregular and its timing cannot be known?

There is no sin upon you for having intercourse with your wife if it later becomes apparent that she was menstruating, because you did not intentionally violate the prohibition. You are not required to refrain from intercourse with her unless the presence of menstruation is confirmed. As for your wife, she is considered to be suffering from irregular bleeding (istihada) because the bleeding exceeded 15 days. She should refer to her usual habit, if one exists; what coincides with her habit is menstruation, and anything beyond that is irregular bleeding, for which she should perform a ritual bath (ghusl (definition)) and ablution (wudu) for each prayer. If she can distinguish between types of blood, then black blood is menstruation (between one day and one night and 15 days), and red blood is irregular bleeding. If she has neither a habit nor the ability to distinguish, then she is considered to be menstruating for six or seven days, like most women, after which she should perform a ritual bath and do what a woman with irregular bleeding does.