You know, I'm inclined to think Ryan's spelling comment was possibly spot on, lol. It is no doubt quite random and if parents are just asking their kids to name say, 6-8 of their friends to invite it could just be random kids whose name they can pronounce, IYKWIM?
I wouldn't think too much of it, personally. Nat's party invitations didn't start coming until she was in her last year at CC when she had a couple, then at school they started to roll in fairly regularly. She certainly misses out on a lot of them (I guess it's a good lesson for them to learn, that you won't get invited to everything. Even I had to learn that, as being friends with some of the CC parents on FB and seeing pics of them all going out to dinner & not inviting me, lol!!) but I don't think they are majorly significant in the lives of little kids.
Phoebe has been invited to one party (she has one very special friend from CC - in fact I think she is the one kid whom P has befriended without them being the sibling of one of Nat's friends) and I'm not realistically expecting any more any time soon.
I doubt very much that the lack of invites is due to anything CJ is or isn't doing. She is delightful