What a beautiful request you have brought before the Lord. The cry of your heart for this woman and for all those in her life reflects the very compassion of Jesus, who is not willing that any should perish. He hears you.
Remember how the Scriptures tell us that salvation has often come to a whole household because of the faith and prayers of one person. Think of the godly mother of Timothy, a woman of sincere faith, whose belief passed powerfully to her son. Or consider Lydia, a businesswoman whose heart the Lord opened, and her entire household was baptized. Your prayers are planting seeds like these, entrusting the harvest to God alone. For as the power of sin entered the world through one act, so the power of salvation entered through one perfect life. The Seed of the woman, Jesus Christ, has crushed the serpent’s head. Salvation is from the Lord, and His name, Jehoshua, declares the truth: He has become our salvation.
I am so often struck by the tenderness with which Jesus sought out those the world would have cast aside. I think of the Samaritan woman at the well. She had made a complete shambles of her life, going through five marriages and then simply living with a man outside of any covenant. Yet to her, a woman with a ruined reputation, Jesus chose to reveal Himself directly for the first time as the Messiah. "I who speak to you am he." He did not shy away from her past; He offered her living water. He did the same with the woman caught in the very act of adultery. Facing a crowd ready to stone her, He showed a profound grace, saying, "Neither do I condemn thee; go, and sin no more." He is able to save to the uttermost anyone who comes to God by Him.
This is why you can pray with such confidence. The thief on the cross had nothing to offer in his final hour but a plea: "Lord, remember me." That simple cry of faith brought him instant salvation. It was a gift of God, not something he could earn. Your request is a prayer that this same gift of faith would dawn in the heart of this woman and her circle. You are, in a sense, like the persistent widow before the unjust judge, bringing your case daily before the Righteous Judge who loves to answer.
So do not stop praying. Do not stop believing God for their salvation. Paul and Silas, locked in a dungeon, sang praises in the darkest hour, and their witness brought a jailer and his whole family to the point of asking, "What must I do to be saved?" Your faithful prayers, lifted up to the Most High God who shows us the way of salvation, are a powerful witness. He has covered you with the garments of salvation, and the horn of His saving power is still raised in the house of His servant. Trust that the God who did not rest until His purpose was accomplished will hear your intercession.