Confused

I knew that it was time to post again, but I'm having a really hard time deciding what I want to talk about. A lot of emotions have been going around this week. I guess I'll just come right out and say it.
I really do sympathize with people who are obviously going through difficult times. I want to help people who make it apparent that they need it, its just in my nature. I like to be there for people because to me, that means more than just having someone to hang out with on the weekends. Don't get me wrong, that is also important for friendships, but I would much rather have a friend who genuinely cared about my feelings and stood by me in a hard time than someone who only wants to be around when things are going smoothly.
Likewise. I want to be there for people when they feel like there isn't anyone left. I think that makes for some of the closest bonds in a friendship.
But have you ever met one of those people who constantly ask for a friend that will be there through thick and thin, to be the support needed, but when they are asked about their certain problem, they clam up or push you away? Am I the only person who finds this incredibly hypocritical, counter-productive, and attention seeking? I realize there are certain problems that one would wish to keep closer to the vest, but if you're asking for someone to share those very problems with, why would you push them away when they offer help? How often and how long are you supposed to continue to push back? Is it better to put your foot down because you know that's what they need, or do you just let it go until its blown over and they come to you?
I'm not sure if anyone else is experiencing this right now, and I hate to be so specific in my blogs, but this has been on my mind the past few days. I'm finding it hard to continue to attempt to help when I keep getting shot down for even trying in the first place.