In "olden days" personal hygiene left much room for improvement. As a result, many people 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, we have the expression "losing face."