Heres my take on why so many people quit bjj at white belt and unfortunately blue belt too. Like he said it takes a type of mental toughness that some people just don't have. Now I was one of the top 5 and id say probably top 3 white belts in my academy, so i dealt a lot of ass whoppings and didnt recieve nearly as many as I gave out in the whitebelt class. In my gym because were so stingy on belt promotions, once youve achieved 4 stripes on your white belt, you are moved to the advanced class. The amount of ass whoppings I took in the advanced class is definitely enough to get someone to quit. It takes a lot to go in and know that you're about to be beaten in so many ways, and you can hardly stop it at that point. Most of the people I was white belts with quit, but quite a few of us were promoted to blue belt (14 of us, and the academy can't think of a larger group of whitebelts to be promoted to blue).
Blue belt is a point where a lot of people quit too, because they were chasing that blue belt at white belt. Now of course it felt amazing that day I got promoted and all of the people coming up to me congradulating me and telling me they thought I was a blue belt already, but after that faded in a couple days and it felt like just prior to me being promoted. A lot of people quit shortly after it fades because of that. They realize belt doesnt matter much and they lose interest. It takes on average 8-12 years to get a black belt in BJJ. Some gyms less and some gyms more (my gym is one of those thats more). Generally once someone makes it to purple belt (4-6 years), they usually are in it for the long haul, but not always.
BJJ is also one of those martial arts thats VERY taxing on the body. While were not kicking eachother in the head, we are choking and bending joints in ways they were not supposed to go. Judo, BJJ, Wrestling, Mauy Thai and kick boxing also fall into the same category and re very legit.