After seeing Ben's post, I went looking in my dictionary, then went back and re-read the whole topic.
I think forgiveness is in the first instance more important to the forgiver, because it should represent something they are giving up: namely some sort of claim of redress on actions by another. The importance of forgiveness to the recpient is that the forgiver has intentionally foregone this claim and thus can proceed to interact with the forgiver largely as if the prior transgression had not occurred. If the recipient of forgiveness makes the same transgression, than they are abusing the forgiveness. This is likely to make the other party either reluctant to forgive, or completely prevent forgiveness until restitution is met.
Note that I don't believe forgiveness can be offered "instantly". Sometimes it may take a long time to forgive someone something.
Wade.