I moved after 2nd, 6th, and 9th grade. Luckily I have brothers close to my age. It's definitely impacted me and made close friendships confusing. I talk to people easily in public or when I run into them, but I don't think I'm on anyone invitation list outside of family.
I've made the concious decision to keep my children in the same school, despite moving several times in the same area since I rent.
Growing up I had problems fitting in and also experienced this sense of loss; not having the same shared experiences as people around me. I wonder now how other kids who "didn't fit in" for whatever reason (orientation, intelligence, economic status) feel? Or is everyone alienated to some extent, and just hides it?
I feel like I fit that grouping too. I didn't fit in most places as a kid (I never really figured out why, which still scares me), but I had a pretty good group of friends in elementary school who bonded over that fact. Unfortunately our middle school split each grade into two "teams", and I ended up on the wrong one. That meant I had none of the same classes, my locker was in a different hallway, and I had a different lunch period. Essentially, it was like I had moved. Thanks to that, middle school is the most forgettable time of my life. I sort of made a few more connections throughout those years, but nothing that lasted at all, and any time i've talked with those people since has been pretty awkward because we never really knew each other.
Luckily that changed with high school, where more freedom was offered and so I found new friendships easier to make. I was eventually able to make at few friends, one of whom has been lifelong, by random happenstance of lunch tables. Interestingly, my wife had roughly the same experience of losing all her friends at the start of middle school and not really rebuilding until high school.
I've made the concious decision to keep my children in the same school, despite moving several times in the same area since I rent.