"Can, or cannot, Young Goodman Brown be forgiven for living the rest of his life as he did and why?"
The concept of forgiveness depends on who is giving the forgiveness. Are you asking if Brown can be or should be forgiven by God, or are you asking can he be forgiven by the people he lived with in his day to day life?
God will forgive Young Goodman Brown for the sin of anger, abandonment, and any sin for which Brown asks forgiveness. However, Brown turns his back on God. Without our faith in God and our plea to Him for forgiveness there is none.
"Often, awakening suddenly at midnight, he shrank from the bosom of Faith, and at morning or eventide, when the family knelt down at prayer, he scowled, and muttered to himself, and gazed at his wife, and turned away."
The people in his life may not be forgiving. The reader must remember that this character is disillusioned. He has gone into the woods, lured by the devil, and sees everyone he respected and loved there worshiping evil. Goodman Brown was horrified to see that the people he beleived to be pure and holy were marked with the blackness of sin. He couldn't overcome this disillusionment. Even the woman he loved, Faith, was not pure and holy as he first believed. How could he find his way back to the love and respect he once held for these people?
The higher the pedestal that we put people up on top of, the farther they will fall in our eyes when they disappoint us; and they will eventually disappoint us. We are all human, and
"Brown's illusions about the goodness of his society are crushed when he discovers that many of his fellow townspeople, including religious leaders and his wife, are attending a Black Mass. At the end of the story, it is not clear whether Brown's experience was nightmare or reality, but the results are nonetheless the same. Brown is unable to forgive the possibility of evil in his loved ones and as a result spends the rest of his life in desperate loneliness and gloom."