I'm not sure that they were "temporary" absences because the kid never returned home after going there (unlike a college absence). 

What about the support test? If my client's health insurance provider and Medicaid were paying for the kid's room and board for Jan 1 - early July (when my client legally dissolved the parental relationship with the kid), it seems that my client didn't really pay for more than one half of his support either. Thoughts?