I find the question is representative of a kind of company culture. The startup-mentality, go-for-broke type companies are looking for "ninjas", "superheroes", "geniuses" and so on. They want their employees to live and breath their work, and if we're not being particularly generous about it, they want this because it benefits them. Remember that if we're talking about full-time engineers, these people are doing somewhere around 30-40 hours of developmental work a week. That's a significant amount of time learning and improving as one solves problems and exercises their muscles. I would suggest stagnation would only occur if you got away from development entirely - say if you moved into a management and were organizing a project rather than spending time in the code.
I know lots of people who work at work and do other things entirely at home. One thing I want to bring up: The question asks if people who don't program can continue to improve. If we answer yes, then we're biasing towards people who have the time and energy to do so, and saying that those who don't have no hope of growth.
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