Luther writes about “Abba, Father” in Galatians 4:6:
The lips say nothing, but the heart says something like this: ‘Although I am oppressed with anguish and fear on every side and seem to be forsaken and utterly cast away from your presence, I am still your child, and you are my Father, and for Christ’s sake. I am loved because of the Beloved.’
In serious temptations, when the conscience is wrestling with the judgment of God, it is inclined to call God not a Father but an unjust, angry, cruel tyrant and judge. And this crying, which Satan stirs up in our hearts, is felt strongly, for it seems then that God has forsaken us and will throw us down into hell. (See Psalm 31:12, 22.)
This is not the groaning that cries ‘Abba, Father’ but the roaring of God’s wrath. This is the time to turn your eyes away from the law and from the sense of your own conscience and to instead lay hold by faith on the promise, the word of grace and life that raises the conscience up again so that it begins to groan and say, ‘Although the law accuses me, and sin and death make me ever so afraid, yet, O my God, you promise grace, righteousness, and everlasting life through Jesus Christ.’ And so the promise brings a sighing, and groaning, which cries, ‘Abba, Father.’
Alister McGrath and J. I. Packer, eds., Galatians by Martin Luther (Wheaton, IL: Crossway, 1998), 209.