In John 16:7-11, Jesus outlined the work of the Holy Spirit, when he said:
Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. And when he is come,he will reprove the world of sin, and of righteousness, and of judgment:
Of sin, because they believe not on me; Of righteousness, because I go to my Father, and ye see me no more; Of judgment, because the prince of this world is judged.
Thus there is only one sin that can't be forgiven - "... they believe not in me". It can't be forgiven because the perpetrators won't have it, and they won't have it because to their rational mind such an idea is either a stumbling block or foolishness.
Jesus said in John 10:9,
I am the door: by me if any man enter in, he shall be saved, and shall go in and out, and find pasture.
The 'brother' in 1 John 5:16 is anyone who has stepped through the door. If he has stepped through the door, then he can be reasoned with in regard to the commandments - God's principles of life for this creation - because they will matter to him. If he hasn't stepped through the door, then he isn't a brother, and your reasoning will be as pearls cast before swine.
What, then, do you do for a non-brother?
Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.
You live the Commandments, which is what the world doesn't do, and why it's in the pickle that it is.