What Does the Bible Say About Church Discipline?

God disciplines us lovingly, for our good.

Hebrews 12:5-11 - ⁵My son, do not regard lightly the discipline of the Lord, Nor faint when you are reproved by Him; ⁶for those whom the Lord loves He disciplines, and He scourges every son whom He receives. ⁷It is for discipline that you endure; God deals with you as with sons; for what son is there whom his father does not discipline? ⁸But if you are without discipline, of which all have become partakers, then you are illegitimate children and not sons. ⁹Furthermore, we had earthly fathers to discipline us, and we respected them; shall we not much rather be subject to the Father of spirits, and live? ¹⁰For they disciplined us for a short time as seemed best to them, but He disciplines us for our good, so that we may share His holiness. ¹¹All discipline for the moment seems not to be joyful, but sorrowful; yet to those who have been trained by it, afterwards it yields the peaceful fruit of righteousness.

God's motive in disciplining us is His love for us (v6).

We know intuitively as parents that love is not always lenient - love doesn't always let. If I let my daughter touch a hot stove repeatedly without disciplining her, I am not loving her enough to keep her from burning herself. My discipline, or lack thereof, reflects on the quality and extent of my love for her.
In the same way, if God lets us continue to commit the same sin with impunity, He is not loving us enough to teach us the importance of avoiding the burn of sin.
It follows that if a church member sees his brother sinning continually and says or does nothing, that lack of discipline reflects poorly on the quality and extent of the member's love for his brother.