No, you shouldn’t give up, even when nothing seems to change in your sister’s attitude. If you quit trying she’ll almost certainly never reach out to you — but if you keep trying, there always is hope.
After all, don’t forget how God has changed your own attitude. For years you wanted nothing to do with your sister — but in time God overcame your pride and bitterness, and now you care for your sister and want to “forgive and forget” the hurts of the past. If God did that in your life, can’t He also do it in your sister’s life? Of course He can — and that should be your prayer. The Bible says that God “is able to do immeasurably more than all we ask or imagine” (Ephesians 3:20).
Pray for your sister, that God will not only change her attitude toward you but also help her realize her need for Christ’s forgiveness and mercy. And if she does reach out to you in some way, ask God to help you respond with love and grace, instead of dredging up the past.
If possible, I suggest you also seek out someone who knows both you and your sister. Let them know what’s been happening in your life and ask them to share your concern with your sister. She might not respond immediately, but perhaps a seed will be planted that will bear fruit later on.