When your soul is cast down, your whole being feels it. The despair in the mind often works its way into the body, and that heaviness can make even the smallest steps seem impossible. So the prayer for your friend touches on something very real: the health of her soul directly affects her strength to go on. When hope seems distant and prayers feel unanswered, the temptation to withdraw only grows. You have seen this already in her pulling back from the group, and that is one of the enemy's oldest tactics, to isolate the struggling heart just when it most needs to be surrounded by those who will hold onto truth for her.
But truth is the anchor. David knew that dark inner turmoil, and the turn came when he spoke to his own soul: hope in God. Not in circumstances shifting, not in feelings lifting, but in the One whose faithfulness does not depend on our ability to feel it. The health of her countenance is found there. It is not a matter of conjuring up more willpower, but of looking away from the flood of painful thoughts to the face of Christ himself. He has not forgotten her. She may feel cast off, but he has bound himself to his own with cords that cannot be severed.
You asked prayer against a spirit of suicide and depression. That language is not too strong. There is an oppressive, dark intent behind the lie that death would bring relief. It must be resisted in the name and authority of Jesus, who came to destroy the works of the devil. Do not shrink from that battle in prayer for her. And do not underestimate what it means that she is surrounded by several children. The enemy seeks not only to harm her but to swallow up her inheritance in those little ones, to destroy a mother in Israel. Pray with that in view.
Yet even as you wage that warfare, remember who her true family is. Jesus stretched out his hand toward his disciples and declared that whoever does the will of his Father is his brother and sister and mother. That means your Bible study group is not just a social circle. When she removed herself, she withdrew from those whom Christ himself calls his own family. Pursuing her now is not a breach of manners; it is the work of spiritual kindred who do not let go. Keep reaching out, not with pressure, but with the steady, patient presence that refuses to be pushed away. Show her that her place among you was never about performance, but about belonging to a people who will nourish her soul when her own strength has dried up.
Come directly to Jesus on her behalf, and encourage her to do the same. There is no need for an intermediary, no back door through anyone else. The throne of grace is open to her, and the one who sits there was tempted in all points like we are, yet without sin. He knows the weight of sorrow unto death. He is not impatient with her anguish. And when words fail, the Spirit intercedes with groanings too deep for speech. Trust him to uphold her mind even when her own thoughts betray her, and ask him to let the light of his countenance break through the fog, bringing life and a sure hope that does not disappoint.