Peeples, I have had experience with this type of person.
Before, I would call, maybe write a note, tell the person, "I'm here if you need me"...and I would never hear anything.
I found it to be very frustrating.
Today I'm not the same person I was back then. As life keeps passing by, I have found I just don't have it in me anymore to keep approaching people like that. I have also found they do not change.
So, now, I just leave them alone. I no longer ask how he/she is, because they burr up and cut you off, or, like you wrote, 'push' me away.
It's just not worth it. Life is too short, and I now desire to live, not approach those who have no desire to be helped. I just leave them to themselves, and, because I'm a Christian, I just ask God to handle them.
Thanks for the question. Blessings, Sparklea