Pertinacity means stubborn, willful persistence in rejecting Catholic truth, even after being shown that the belief contradicts Church teaching.
It is what distinguishes:
Material heresy: when someone holds a false idea unknowingly or innocently,
From formal heresy: when someone knowingly and obstinately refuses to accept a defined dogma.
Only formal heresy separates a person from the Church and results in the loss of grace and membership in the Mystical Body of Christ.