My Wife Refuses Non-Contracepting Sex
What do I do if my wife threatens to leave me if I don't have protected sex with her because another pregnancy is life threatening?
You need to be sure that the medical reasons for it being dangerous for your wife to conceive are well-founded. A good talk with two of you and her doctor would be good, if she allows it. It could be that there is some other personal reason she does not want to have relations with you, in which case—and probably in any case!—you need to have some counseling to foster your loving relationship with each other.
If she refuses to have relations with you without contraception, then it would not be right to insist. You need to pray and show by your kindness and gentle consideration of her that she has nothing to fear from you. If you do not show empathy with her fears, then it is not surprising that she might make such threats. It is your job not to let things reach that point by making sure that she is habitually reassured that you love her and that her needs are uppermost in your heart and mind. Prayer and gentleness will win the day.
Pray to St. Joseph, and don't focus on your frustration at not being able to have relations with her but rather on the hope that when you do finally have relations, she will be participating willingly and lovingly.