I think it's always possible to forgive, regardless of the offense. This may be a view exclusive to me because the word forgiveness is subjective anyway. In my opinion, to forgive is to basically put the offender at ease in a way. In any situation, offender will at some point ask for forgiveness either literally or in a gesture of kindness. This is when the offended has been given the responsibility to answer back, give and take.
Obviously not every act can REALLY be forgiven, but the gesture is necessary especially for social situations where it would benefit more than just yourself to bridge the gap or mend the fracture. There are many situations where one would "forgive" but not really trust at all, but either way this is a social necessity. If another man comes onto my wife and disrespects me, he is on the shit list for the rest of his life. However, if a social situation calls for civility, then of course I will be civil. I will never trust this person with an ounce of anything important to me, however civility is sometimes needed in social situations. It isn't always about the offender and the offended, one must see the bigger picture when the situation calls for it.
Be Christlike folks, turn the cheek but never forget.