Here's one article [1] that found:
"Elevated risks were observed for all examined outcomes, with excess risk seen among those exposed to multiple versus single relocations in a year. Risks grew incrementally with increasing age of exposure to mobility"
Examined outcomes consisted of "attempted suicide, violent criminality, psychiatric illness, substance misuse, and natural and unnatural deaths."
There are many more studies if you search for them that show a range of affects including worse academic performance and one I found that included a higher rate of hospitalization in kids who moved (although the cause was unclear).
It's a traumatic event.
[1] - https://www.ajpmonline.org/article/S0749-3797(16)30118-0/pdf
[2] - http://theconversation.com/moving-home-can-affect-your-child...