We understand that you are going through a challenging time, and we want to lift you and the person you mentioned up in prayer. First, we want to remind you that God cares about our struggles, including mental health issues and depression. He is our refuge and strength, a very present help in trouble. Psalm 46:1 WEB.
In regards to the issues that you are facing, we have to address a few topics in your request. First, it is unclear if either of you have confessed with your mouth the Lord Jesus and believe in your heart that God has raised him from the dead. If you have not done this, there is no other way to be saved. If you are saved, then you can be assured that God is working all things for good for you. This also means that if the person you mentioned is not saved, that you should not be in a relationship with them. Be not unequally yoked with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? 2 Corinthians 6:14 WEB.
We also want to encourage you to seek God's will in this situation. It is commendable that you have tried to help, but remember that God does not call us to do everything on our own. He asks us to surrender our burdens to Him. Cast your burden on Yahweh, and he will sustain you. He will never allow the righteous to be moved. Psalm 55:22 WEB.
It is also important to address the idea of letting go. This person may be a part of your life, but it must be God's will. If you both are saved, you should have a relationship. God does not believe in divorce or being estranged from each other. “It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement: But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.” Matthew 5:31-32 WEB.
Let's pray together:
Dear Heavenly Father,
We come before You, lifting up our brother/sister and the person they mentioned, asking for Your divine intervention. Lord, You know the struggles they are facing, the depression, and the mental health issues. We pray for Your healing touch upon them both. Guide them both, and provide them with the help they need.
Father forgive them for being estranged. We ask for you to remove the reasons that they are estranged if it is your will and their will.
Lord, we also pray for peace and strength. Help them to cast their burdens on You, trusting that You will sustain them. Give them the wisdom to know what they should do and how they can be part of each other's lives.
Finally, Lord, we ask that if they are not saved, that you show them grace, and that they profess with their mouth the Lord Jesus and believe in their heart that God has raised him from the dead.
We ask this in Jesus' name. Amen.
Prayer Focus: God, Thank You. Thank You for loving me. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, mind, soul, body, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
