People don't sneeze in their sleep due to their brain shutting down the reflex.
People actually should be more prone to sneezing during our sleep, as the mucous membranes swell when we lie down. This makes them more sensitive, but there usually isn't as much airflow or movement to stir up irritating particles, so they aren't as exposed to stimulants.
When we're awake, particles, allergies or an illness can stimulate the nerve cells in the nose. The nerves then send signals to the brain in order to initiate a sneeze to get rid of whatever is irritating it.
But during rapid eye movement (REM) sleep, certain neurotransmitters shut down- this state is known as REM atonia. This means that the motor neurons are not being stimulated, so they aren't sending these signals to the brain.