Should I give up on someone who keeps pushing me away?

This is a hard question, because we can’t choose who we love. But also, giving someone space, and letting them come back to you (I hope) can help.

Hard to comment since i dont know the nuances of your relationship. Maybe not view as giving up. Give them space, or send love in your mind and be clear your door is always open for support, but dont expect anything. Sometimes people need space, and have acceptance that some relationships are limited. Take what you can from it if its done, and use that in your future interactions while moving forward. I am going through similar right now. Its tough.