Is it possible my chickenpox vaccine may have failed me?

It happens. When we first started giving the vaccine, one dose at or after a year of age was standard. Data showed that at least 85% developed long term protection.Eventually we began giving 2 doses at 1 and 4-5 years or which brought the long term protection up around 95%. Your doc can run a blood test to see if you have a protective level, but yes, the vaccine doesn't protect everyone.
Yes. Not all vaccines are 100% effective, revaccinate if any concerns.