Fr. Michael (priest at the Holy Nativity Orthodox Church in Canada).
Ostensive Lyme asked whether Christians "need to" forgive the unrepentant. The short answer is yes.
I can see why someone might say no if we think of sin and forgiveness in mere juridical terms. However, as Orthodox Christians, this is not how we understand sin and forgiveness.
As Orthodox Christians we think of sin as wounding and alienation - from God, from others and within ourselves. So forgiveness has to do with reconciliation. Forgiveness has to do with healing. Just as I pointed out in Jesus’ parable of the unforgiving servant, forgiveness is not static. That is, how or whether we receive God’s forgiveness depends a great deal on what we do. It’s a mystery, not a syllogism. God forgives unilaterally and completely. Jesus has already died for the sins of the whole world. From God’s end (so to speak), all of the sins of all of humanity for all of the ages have already been forgiven. But that is not the end of the story. Forgiveness has a life of its own - and anyone who has tried hard to forgive someone who has deeply hurt them knows this by experience.
Somehow the one forgiven interacts with the forgiveness offered. We might even say that the forgiveness offered must take root and grow and bear fruit in the life of the one forgiven. If this does not happen, forgiveness is somehow short circuited - in the one forgiven, not necessarily in the one forgiving. It helps to think of forgiveness as the whole process of healing, not just the initial step, not just a legal absolution or a letting go or forgetting of past wrongs. In relationships with others, one’s willingness or unwillingness to repent affects the progress of forgiveness, of healing. However, whether or not someone repents or accepts forgiveness does not necessarily have any effect on another’s ability to forgive. God forgives completely, even if His forgiveness does not always take root and bear fruit.
Not only does forgiveness interact with the one forgiven, it interacts within the one forgiving. God is perfect, so only God can forgive perfectly, once and for all. Human beings are sinful, which means that within ourselves we experience alienation. Part of us can want to forgive, while another part of us doesn’t, while yet other parts of us remain hidden. We can forgive on Monday and by Wednesday find surging resentment and anger rising from some hidden place within us. Forgiveness, for sinful human beings, is a process.
From the perspective of the one forgiving, the repentance or apparent repentance of the other is irrelevant because you have no control over someone else. In fact, I can’t even know if someone else really is repentant, no matter how penitent they seem. Only God knows that. What I do have control over is myself, and like God - and only with God’s help - I can forgive, I can begin to heal, regardless of the other's repentance or lack thereof.
P.S. It is also possible for one who has committed an offence to experience forgiveness even if someone refuses to forgive him or her. Forgiveness ultimately comes from God. So in forgiving, it's important to realize that the resources necessary to forgive are not our own apart from God. The ability to forgive those who sin against us comes from receiving the forgiveness that God has first given us, and in turn our forgiving others affects our ability to receive God's forgiveness. It' a mystery; it's a process; and it takes a lifetime.