I think it is an important question, which frequently appears in discussions. Do you know any surveys which approach it? What are the reasons for people with completed PhD in mathematics to quit it? Definitely, there are many reasons, but how many of them would like to do research in math, but switch to something else because of uncertainty in the future?
Anyway, what are your expectations of such a survey? I heard many estimates, from 0% to 50%.
By quitting mathematics I mean, that a person stops doing research. So, switching to finance, programming, only teaching without active research means "quitting mathematics" in most cases.
I don't know, we can define "doing mathematics" by writing at least one research article in five years or so. Or working on research positions in academia or Microsoft Research and similar. Any surveys are welcome, in any country and time period.