Why can't I bring myself to pray right after I sin?

This is pride. If we can't approach God when we sin, that is an issue, a psychological issue with us, and projecting human emotions or a human mindset onto God. God is transcendent. He is beyond our emotional states, our emotional whims, and he's way beyond our failures. If we begin to project to God emotionalism that we experience, or disappointment that we experience with ourselves, we are not abiding in a spiritual mindset or state. We have to transcend the emotional. Those who are humble pray and ask the Lord to heal them and to have mercy on them. Those who don't want to approach God are struggling with pride and egotism. God will help you if you are humble. It says in the scriptures, God gives grace unto the humble. Many times people fall into sins, especially serious sins of the flesh, it's due to pride and them turning away from God. And when the temptation strikes and they listen to the inclination and the thoughts from the devil, they don't cut them off with the Jesus prayer. So God is not looking for us to, in a sense, lift the immensity of these sins on our own, but wants to help us. But we have to be humble. If a person is humble and continually repenting before God, these serious sins will go away.