Strokes in the lateral medulla can abolish the sneeze reflex
but in association with other signs of stroke such as clumsiness, weakness or sensoru loss, or inability to swallow
a reflex has both afferent (incoming to the nervous system)) and efferent (outgoing) components. An interuption can occur at any point, not necessarily in the brain, and block the final response. So, for instance the problem could be with your sensation of the insult that trigger the sneeze.