I understand that the academics can be mind-numbing for a non-skipped child and that lack of a skip creates its own problems. It's just that I advise against considering only academics when considering a skip, or allowing yourself to be swayed by enthusiasm of others. In other words, weigh lots of factors carefully.
I agree with Val on this - sorry I can't give you a straight-up positive story, but you did ask for cautionary too. My caution doesn't come from my own children - we chose not to grade accelerate based on the experiiences of friends' children who'd been 1-2 grades accelerated early on, in early-mid elementary, with parents enthusiastic and eager for the advanced academics, only to have the parents begin to regret the decision as their children went through middle school and on into high school because of the age difference compared to classroom peers. If your dd is excited about the skip, II'd definitely consider it, but I would first think through how you feel about potential social situations - puberty/hormones/school dances/dating/friends having drivers licenses etc. Consider where you think she's at in terms of sexual awareness etc - is she ready for all that comes with kids - friends and boys who might want to date her - moving through puberty (personality can be really significant here). After you have your own thoughts sorted out, if you feel you're ok with the skip in terms of both social and academic situation, talk to your dd about the full circle of what moving up again means - when will she be dating/driving/etc compared to the other kids in her class, how will she feel about that, what rules will you have re riding with friends driving etc and how will she feel about it - all of those things.
Academics in grade school were incredibly frustrating at times for 2 of my kids - the pace of classroom discussion was slow, they couldn't learn at their own speed, and my ds in particular was very annoyed by being in class with students who didn't "get it" as quickly as he did. Once they reached middle school, however, subject acceleration became an option and once they hit high school it was much easier to find programs and classes that met their needs without requiring grade skips.
So - coming back around to academics, it sounds like the issue with your dd started with subject acceleration in math as the primary need. How does your dd feel about the other subjects she's in at school? Does she feel bored etc? How does she think things will be different by skipping a grade with respect to science, history, language arts etc? There are also other things you might want to consider (depending on your dd's interests) - for instance, if she's in band, is the high school band competitive? Will she potentially not get into the upper level band as soon as she would have if she stayed in her current grade and had one more year of middle school band? (I know that might sound beyond silly to some, but the whole key is - this is a very individual situation.) I would also ask your dd what it is she wants from skipping another grade. Be sure you understand what it means to her, and that that is something you feel is a reasonable expectation. One thing my kids found out through subject acceleration is - just because you've moved up a technical level, doesn't mean you've moved up into a classroom with kids who are all thinking as quickly as you'd like. Ultimately for my kids, the thing that made the most impact in their education was being placed in gifted classrooms with high ability students, rather than specific grade level.
Last thing I'll add is what ultimately made the difference for me in deciding not to have my kids skip - I don't want them leaving home before they have to. Sounds hopelessly selfish I'm sure, but I only have this one set of kids to raise, and once they get to high school you really realize how quickly our time with them at home passes. I'd give anything to add on years of high school just to have them home longer... maybe they aren't as far ahead technically in math or science or whatever as some equally-capable other kids are, but in spite of not skipping and having had those elementary years of academic frustration, they haven't lost their love for learning and they haven't lost their motivation. The key for them was more in finding engaging classrooms and equally capable peers when possible rather than simply grade-skipping up the ladder.
Please know I'm not trying to be discouraging - just offering you a few things to think through. Chances are if your dd wants to do the skip and the school says she's ready, she's ready. If you think it through and are comfortable with it, do it and don't look back - she'll be fine.
Best wishes,
polarbear
