What is the ruling of Islamic law on a sick woman using contraceptives, given that doctors believe a fourth pregnancy would endanger her health?

It is permissible to seek assistance from a disbelieving female doctor if she is trustworthy and not accused. Permanent birth control is not permissible unless there is an extreme danger to the woman's life or severe harm from pregnancy that cannot be overcome. If the harm is temporary, temporary birth control methods may be used. If doctors disagree, the opinion of the most knowledgeable is taken, then that of the majority, and then that of whoever reports what was hidden from others.