It depends on how you define "gifted adult".
I was certainly "gifted" for academic labelling purposes as a child.
However, I'm not an "high achieving" adult and have never had interest, even though I was given the opportunity to go on to grad school, it just wasn't my thing. I feel that the awesome support I was given as a PERSON (rather than a test score) helped me realize that it wasn't my thing and kept me from being hung up on numbers and percentages as my identity. I know quite a few of my fellow gifted kids who felt like catastrophic failures when they didn't take over the world or get a PhD or whatever it is that they thought they "ought" to do or if they weren't constantly given feedback about their talents/gifts through testing or achieving things on the list. So I do understand your concerns with the labeling. Really though, avoiding the gifted label isn't protection against that (look at the myriad of former cheerleader/star-athlete/loser/geek/whatevers who are always looking back to what they were rather than where they're going). If you ensure that your child has people that they respect that know how to nurture both their gifts AND their person, I think they'll be fine.
I like being totally removed from professional life. It gives me time to think and to be on my own terms. I'm happy and satisfied with my life, even though I have seen people literally react with horror (normally in the context of them talking about their gifted children's achievements) when I mention that I was also labeled gifted (of course, I was also labeled retarded too at one point, but that's a different story)--because I'm not someone discovering the cure for cancer or a juliard graduate...I'm a fat jeans-n-tees housewife whose major post-college accomplishements are hanging out with homeless folks and supporting felons re-enter society and my 3 kids...all of which certainly don't require a high IQ.
So if you are thinking about hard driving achievement oriented as far as gifted adults--then no, I have to say most of the the people I know burnt out long before that (not everyone though). If you are thinking of lifelong facination and devotion to learning for oneself at one's own pace, then yeah, I think most of us do retain some portion of that, regardless of whether or not we're inclined or choose to channel it into outward achievement.
If you're feeling bummed at not having anything to show for your childhood label, I'd encourage you to turn your mind and heart inward. Is there anythign missing in your life that is making you focus on that perceived failure? How could you fix it? (I love that many Ivy League and excellent state universities now offer courses/lectures on DVD/CD, I did that for awhile when I got pangs and found that exercising my mind and listening to some rockin' and amusing professors satisfied me, especially since I had no obligations but to listen and learn and research more if I was moved to do so.)
No one "fails" being gifted. And I don't agree that it's always that someone failed you either. Sometimes the path we end up going down differs radically from what was expected of us or we internalized. You know what? That is okay. If you're not happy with it, the nice thing is that you CAN choose to step off the current path and go a few steps in a different direction and see how you like it. But I would avoid getting hung up on what you may think you're "supposed" to be doing. Think instead of what you are doing, and what you genuinely would like to be doing. If that's some kind of external achievement, that's cool--just put it as your goal and start taking small steps.