If you give up on someone did you ever really love them?

There are different reasons for giving up on someone....the fact is that if you are not going to give up on yourself, sometimes you have to give up on another, even though you continue to love them. I have never stopped loving anyone I ever loved, but in some cases the relationship was not salvageable. I never give up on them as a person, but in some sense I realize that I needed to let go.