I don't know what the percentage might be at my dojo, but I would guess it's reasonably high. I am a green belt, going on 2 years training now. I've seen an awful lot of people start and drop out in that time. And some (perhaps most) were more gifted than me; they caught on faster and it seemed to come much easier to them than to me.
I'm guessing, but I think that a lot of those who quit do so because they find real martial arts training different than what they expected it to be. I'm not sure what they were imagining, but it's a lot of hard, repetitive work, and some of it can be a real slog to get through. Or perhaps they just have different priorities, or maybe their job situation changes or they move away.
I am also told by the more senior members that there have been a number of people who stay long enough to make black belt and then leave, also for reasons unknown. And it takes a lot of dedication to make black belt in my dojo; average time from seven to nine years. To make it that far and then quit kind of baffles me; but this is what I'm told happens. Some quit, I am told, to start their own dojos (even though a Shodan is in no way qualified to teach or promote in our style). Others just stop coming. Some still show up from time to time, maybe a couple times a year, but they've been Shodan or Nidan forever. I guess that's all they want out of the training, which is fine if that's what they want.
On a more general note, it seems to me that people in general have a much lower patience for anything. Everything in our society is based on now, not later. Credit now, college degrees now, martial arts belts now. The very notion that something worth having is worth working hard and patiently waiting for is anathema. One even sees it here on MT to some degree, although I think most here understand that quality training takes time. I've been told that "Seven to nine years to black belt? That's a bit much, don't you think?" No, I don't think so; in fact, I'm rather glad of it. It makes it that much more valuable and real to me. If it wasn't hard to get, what would be the point?
I probably would have been one of those impatient people who wanted everything now not later if it had not been for the Marine Corps. It was there that I learned self-discipline and realized that yes, I can do nearly anything if I want it badly enough and am willing to do what it takes to get there. At the age of 47, I started MA training. I'm not quitting, and younger guys in better shape are starting behind me, catching up to an passing me, and then quitting. I continue to progress. Why? I dunno, I guess because I don't mind pain, I'm not in a hurry, and I know what I want. One foot in front of the other, I just keep plodding towards my goal. And Shodan isn't my goal, either, so I won't stop there.