If I'm stuck in a sin, I need God's grace to get out. And if I'm free of that particular sin, I need God's grace to stay out.
It seems to me that this leaves no room for self-righteousness, because the "saint" is as dependent upon the grace of God as the "sinner." The picture I have in my mind is of two starving people. If one of them finds food and gorges himself, will he then consider himself superior to the other simply because his stomach is full? He's full because he ate food, not because he is a superior person. The other is hungry because he needs food, not because he is inferior. Fullness comes from food, and obedience comes from God's enabling.
So whether we fall or stand, we need God's grace. And "if you think you are standing firm, be careful that you don't fall" (1 Cor. 10.12).