How common is it for a child to die of pneumonia?

Not common: It is not common at all in previously healthy children, but it does happen.

Varies with cause: Pneumonia is a label with variable implications. The average toddler/child is often treated as an outpatient & most heal without complications. Some viral pneumonias would self heal & most bacterial will respond to meds. Rare causes of kid pneumonia include staph & chickenpox, both of which have a higher fatality rate.There are other examples & all fall into the range. Most do well, some die.