When is Hester untrue to the scarlet letter?Nathaniel Hawthorne's The Scarlet Letter

In Chapter
XIII, Hawthorne writes as a separate
paragraph,

The scarlet letter had not done its
office.

In this
chapter, Hawthorne describes how Hester has changed:  The warmth, and passion appear to
have been replaced by distance, severity, and grayness;  her hair has lost its luxuriant
color while her beauty, too, has faded.  Similarly, she retreats from company, isolating
herself, and she acts more like a servant than a nurse when she cares for
others.

Moreover, the repentance that the church leaders
have expected to exact from her is instead a cold despair.  In fact, Hester considers
sending Pearl

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at once to heaven, and go herself to such
futurity as Eternal Justice should
provide.

By the fact that
Hester considers suicide, which is an unpardonable sin in the Puritan code, Hawthorne
indicates that "the scarlet letter has not done its office" and she has been untrue to
her letter.