Is it permissible for a Muslim woman to pray without a head covering due to an excuse?

A mature woman's prayer is not valid unless she covers her awrah, as the Prophet, peace and blessings be upon him, said: "Allah does not accept the prayer of a menstruating woman except with a head covering (khimar)." If she does not find what to cover her awrah with, she should pray according to her circumstances and fear Allah as much as she can.

As for a woman who does not adhere to the hijab outside of prayer, she must perform the prayer at its prescribed time, fulfilling its conditions and pillars. Prayer is an obligation that must not be neglected, no matter how many sins one has committed. The remedy for sin is not to abandon another obligation, but rather through repentance and hastening to it.