DD9 has done 2 separate grade skips and is in need of another, but we are not sure whether or not we will do another one.
She skipped from kinder into 1st grade after a few months at age 5, then this school year she skipped into grade 6 from grade 3. Socially things have gone pretty well, she seems to feel like more kids "get" her in gr 6 than did in grade 3, however she is still not really challenged, she has high As in all of her classes and is currently working on gr 8 math at home. She will be ready for all other gr 8 classes by the time August comes around, but she does not want to skip into a class with even bigger kids than she is with right now.
The first month of the skip this year she was happier than we've seen her in a long time at a school, but as the semester has gone on she has gotten a bit dragged down with the larger volume of work, and the realization that the jump from gr 3 to 6 was still not enough for her. However, she is still happy at school, loves her teachers and has some friends.
We too wonder where the grade skipping will end - she is still very much a 9 year old in her need for a play ground and silliness, but when her brain isn't stimulated she is so miserable that noone, including her, can stand to be around her. We are actively looking at various alternatives, like subject acceleration next year and testing out of classes.