Whoa is me...

As Christians, why do we (meaning me right now) get caught up in the feeling of "how dare they" when someone sins against us or others? Lately I have been struggling with a friend who professes to know the Lord as they're personal savior but the fruits are not so apparent. I should be in deep prayer for this person, instead I am bathing in my bitterness and anger.
I find myself making a joke of the situation so not to be frustrated but deep down I feel like I have done all I can and I should move on before I begin and/or continue to stumble.
Let me say, I do try and help my friend be accountable for their actions, but I am quickly frustrated when I do not see an immediate change. I think I have an idea of how our Father feels when we continually beat our heads up against the same wall when He's lovingly commanding us to stop :-)
It's funny how quickly we give up on people not remembering how broken we use to be and at many times, still are. At what point is it ok to "give up"? I read Matthew 18:15 "If your brother sins against you, go and tell him his fault, between you and him alone........ " and try to check myself and my heart to make sure that I AM doing everything I should and could be. This is a hard question for me because I am really not sure.
I try to remind myself that no matter what is done or happens to me, I never receive more than I deserve and every situation in one that will help me grow in my faith. I also try to remember, although lately this has been hard, that I am not fit nor do I have the authority to judge my friends heart.