Not that many people, according to a recent, somewhat provocative and perceptive Streatham & Brixton chess blog.
I have to admit that upon first impression, I considered the post to be in the tiresome naysayer category regarding adult chess improvement. That said, I further have to admit that they're probably right, at least in terms of the average tournament chessplayer. I recently attended a chess event where it was apparent that serious training was not really part of anyone's agenda, including the idea of systematically learning from your mistakes (or even just learning). Nothing wrong with just enjoying things, of course, and perhaps sometimes wishing you were better. But as Mark Twain said, "Everyone talks about the weather, but nobody does anything about it."
I've posted several times before on the general topic and continue to consider the time/energy factor as paramount in explaining rating advancement (the visible aspect of improving your playing strength). The strong, rapidly advancing tween and teen (or younger) players typically sink several hours a day into systematically organized studies, often with professional-level coaches who guide their progress, for a period of years. Adults with jobs and other responsibilities (again, typically) simply don't have that kind of time or energy. (Even if you believe Michael de la Maza's story of how he advanced rapidly, that was in the context of an extended spell of unemployment and nothing else to do.) In addition, the fact that kids can learn more rapidly than adults due to their brains' neural structures (i.e. their greater plasiticity) is certainly a benefit for them, but is too often cited as a cop-out for adult learning.
For those of us with a mix of responsibilities and other life interests, I think the best we can shoot for is to designate around an average of 30 minutes - 1 hour per day for mindful study, surge around tournament time or when we have more time, energy and motivation available, and take meaningful breaks from chess when necessary to clear our heads. This all should be doable, although it still takes discipline and commitment.