Personal hygiene left much room for improvement in the 1700s. As a result, many women and men had developed acne scars by adulthood. The women would spread bee's wax over their facial skin to smooth out their complexions. When they were speaking to each other, if a woman began to stare at another woman's face she was told, "mind your own bee's wax."
Should the woman smile, the wax would crack, hence the term, "crack a smile."
In addition, when they sat too close to the fire, the wax would melt...therefore, the expression losing face."