Hi J.,
It sounds like your son has both a general "issue" with self-motivation and problems with physical endurance. It's likely that both are behavioral, but it couldn't hurt to rule out a physiological cause as well. I always thought my son was lazy until we found out that he was growth-hormone deficient (I'm not suggesting that this is the case for your son, BTW). It turned out that "laziness" was really just lack of energy because of the hormonal deficit. Later, we found that the initial GH deficiency was actually a first symptom of Crohn's disease, and lack of energy was also a result of his body not being able to properly digest and absorb nutrients from food. He struggled with this all through his preteen/adolescent years and into his early adulthood. Now that he's on a completely gluten-free diet and vitamin supplements (he's 22 and has been on it for a year), I can't believe how much greater his energy levels are AND his ability to self motivate -- without the need for other medication.
There's been a lot of research of late surrounding gluten sensitivity and gluten intolerance. It's much more prevalent in populations of European and Middle Eastern descent than once realized, and it can lead to a whole host of metabolic problems. Consider removing gluten from your son's diet for a couple of weeks, and see if his energy levels increase. This means no cereal grains at all, including wheat, corn, millet, barley, oats, spelt, and rye, and product derived from them (especially corn syrup, which is a leading contributor to the general rise in obesity in the U.S.) Substitute brown rice and sweet potatoes or yams (avoid white potatoes as much as possible: the carbs in them are more complex than white cereal products, but still not as metabolically utilizable as those in sweet potatoes and yams, which also have a higher protein content).
At the same time, you might try having him see a child psychologist and/or family counselor for a few sessions to see if a professional can help you and him get to the root of his motivational issues. The counselor can also help you set up an external motivational system that you and he and stick to. You're right -- letting him quit has set a precedent, but that can be set aside! Also, what things does he like to do now? Does he enjoy art? Music? Science? If he's got an issue with fear of failure, work on it with pro, but also explore things that he feels comfortable with, maybe even "oddball" activities that most kids don't do so the competition isn't as fierce, but still seem cool. As an example, Fencing is one of my favorite sports, but it's not a popular sport in the U.S., so the competitive field is small. But, it's a lot of fun, physically demanding, but in short bursts, and has kind of a swashbuckling/fantasy cool factor that can be very attractive to a kid. It's also an individual sport and doesn't require being able to keep up with a team. The same goes for things like gymnastics, swimming, and tennis. In terms of non-sports extracurriculars, might he enjoy something like art or music classes, a robotics club, a creative writing class, etc? Engage him in thinking out-of-the-box with you.
One last suggestion I have is to sign him up for Boy Scouts. Scouting offers a wide variety of very fun activities, from athletic to academic, that let a kid explore and figure out what he likes to do. Find a good troop with a focus that interests your son. Most troops will combine physical activity (especially camping and outdoor skills that include things like rafting and rock climbing) with service work, horseplay, and merit badge work.
Good luck -- I know it's not easy!