Our Gemara on Amud Beis discusses the laws of the vessels in which the meat of sin offerings was cooked. A copper vessel is scoured and rinsed in the grounds of the Temple courtyard, while an earthenware vessel must be shattered.

Kli Yakkar (Vayikra 6:21) adds a symbolic dimension. While this rule applies to many sacrifices, the sin offering is the source text. The Kli Yakkar reads significance in this, seeing a special emphasis and message to the sinner.

The human body is a vessel too, for our souls and personality. And just as some materials absorb matter more permanently than others—such as the earthenware that cannot be purged, while the copper can—so too with people. For some, the transgression occurs but does not become embedded into the soul or character, and so a relatively simple repentance is sufficient. The cleansing water of the copper vessel is analogous to the cleansing effect of Torah. Studying Torah and refocusing is enough for some to recover from a momentary lapse or loss of commitment. For others, the effects of the sin penetrate deeper, and for full repentance, there must be a shattering. The person must break down rationalizations, defenses, and distorted beliefs or expectations in order to become free from the trap of sin.

Kli Yakkar does not explain the specific factors that make one more susceptible to the more permanent absorption of sin, but I would imagine frequency, intensity of attachment to the sin, general piety, and rapidity of remorse are logical contributors.