I had a nasty case when I was young, and a nasty case again as an adult, and if that's any indication that I don't in fact have an immunity to that illness, I'll report if it comes back a THIRD time. My mother also had nasty chicken pox twice. Some folks have gaps in the normal immune system.
To my knowledge, I have never had chickenpox and I am 66. My brother had it bad and we shared a room, I didn't get it. My daughter had it bad and I didn't get it. I have been waiting to get shingles which would prove that I had a very light case but so far nothing, now I read that people are getting it multiple times. Strange.