• primary vaccine failure: This is when a person fails to produce antibodies (at detectable levels) or does not produce enough antibodies considered necessary to protect from the disease.

• secondary vaccine failure: This is when a person does produce antibodies in response to vaccination however the levels wane and decline at a faster rate than normally expected. However, antibodies to almost all vaccines decline over time, even after booster shots, so secondary vaccine failure in outbreaks of disease amongst the vaccinated is frequent.

You can find examples of failures here: vaccine failure and secondary vaccine failure.

Another thing to note is that disease occurs even when a person has more antibodies than deemed sufficient to prevent disease. You can see examples of that here.