Is the mother remiss in her duty towards her son who drowned, and who used to run away from home and neglect his studies and prayers, and what is her recompense?

If the repeated escape of the child did not result from the mother's negligence in his custody, then she is not religiously responsible for his death by drowning; because a person is held accountable for his actions or for causing them, and what befell the child is a calamity that expiates the mother's sins and transgressions. The Quranic verses indicate that a person is only held accountable for his effort and deed, and does not bear the burden of another.