Medial longitudinal Arch age stablization.

It seems to depend on what source you read as to when the MLA (medial longitudinal arch) stabilizes, but here is a number, between 7-9 years old. 

Conclusions: The MLA of children remained stable from 7 to 9 years old. Gender and the type of footwear worn during childhood may influence MLA development.

Reference:

Medial Longitudinal Arch Development of Children Aged 7 to 9 Years: A Longitudinal Investigation.Jasper W.K. Tong, Pui W. Kong Journal of American Physical Therapy Assoc.   DOI: 10.2522/ptj.20150192 Published February 18, 2016

http://ptjournal.apta.org/content/early/2016/02/17/ptj.20150192