My son was tested for diabetes insipidus. The symptoms I was told to look for are extreme thirst and extreme urination which leads to dehydration. To my knowledge it is not related to infections but my son is eight and not as young as your grand child. Maybe that changes the symptoms.
Diabetes insipidus(water diabetes) is due to a hormone lacking that helps us hold onto water, these children will urinate excessively, drink excessively, lose weight and be sick with high sodiums, there is a form due to the pituitary hormone lacking and that which is due to the kidney not responding to the normal hormone.
It does not sound like repeated fevers alone is diabetes insipidus. High white count and fevers that are a mystery needs evaluated by a pediatric infectious disease specialist if the pediatrician has looked at all infectious avenues(kidneys, lungs, throat, skin etc.)