All perfect praise be to Allah, The Lord of the Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If a trustworthy doctor was of the view that the pregnancy of a certain woman at a certain age would usually subject her to more harm and illness, in addition to her other health problems that jeopardize the safety of her pregnancy, then there is no harm in tying her tubes to preserve her life, which is among the higher objectives of Islamic Law.
Moreover, Resolution No.(35)(5/1) of the International Islamic Fiqh Academy reads: " Sterilization (Tubal occlusion for women and vasectomy for men) is forbidden so long as there is no need for it" And Allah knows best.