Is it permissible for a pregnant woman who miscarried one of her twins in the first month, and the bleeding continued until the fourth month, to pray despite the presence of blood?

If the fetus falls and the human form becomes apparent in it, then its blood is nifas (definition) blood, for which prayer is prohibited for 40 days, unless the bleeding stops before that. The human form becomes apparent after 81 days of pregnancy. Before that, the blood is irregular bleeding (dam fasad wa 'illah) which does not prevent prayer and is not considered nifas or menses. So, if the wife miscarries in the first month, the blood discharged is irregular bleeding (dam 'illah wa fasad), and she must pray and make up for any prayers she missed.