Based on people I know, which is a small sample set, Id estimate the drop out rate is around 90% after a year. It also depends on the definition of dropping out, people have different goals, but if we define not dropping out as sticking with it for at least two years, and performing publicly in some way, which seems a minimum threshold, id still say 90% minimum.
I think the main reason is the first 3-6 months of learning the theremin is frustrating, with a steep learning curve. There is no instant gratification, it is difficult enough to play a scale or a simple melody.
Probably 1% or less, become good players, that make a name for themselves, or what have you, but that is true of any instrument mostly. Probably far less than 1% of people who pick up a guitar become classically trained famous musicians, 80% are probably sitting around a campfire 10 years later, playing the same covers of 4 chord songs. But you wouldn't say they dropped out, necessarily. But you dont have most people who buy theremins breaking out their instrument at parties 5 years later to play somewhere over the rainbow for their guests.
If you wanted a closer estimate to an exact percentage, you could take the number of etherwaves manufactured and divide by the number of thereminists you can find, times some fudge factor for the ones who have no web presence.