I have tires with kevlar (specialized armadillo) and have not gotten a single flat from glass, rocks, or thorns. They're pretty good at preventing flats from outside objects (I've pulled out numerous pieces of glass and rock embedded in the outside). However it did not prevent the flat that happened when I overinflated the tube. Always carry a spare tube if you don't want to walk home.

As for the OP's problem, check the rim and rim tape to make sure nothing the inside is causing the puncture.