I have to disagree with that. I've met many people, especially in larger enterprises, who started in development but then became more abstract over time. They weren't bad people, in fact, they were excellent at their job.
Programming to me has never been something that has to be continually pursued in order to stay fluent or able, but merely something that reflects your more basic skills and talents.
It's like playing a musical instrument. Almost anyone can learn playing the guitar, but it takes a special talent to excel at it. For the guitar this requires hearing, sense of rhythm, and others; for programming, this is analytical thinking, systematic thinking, and more. Some people will try to program but never be really good at it. I studied with people like that. It's not their fault, their skills are just in another area. Some others are great at it. Once they learned, it doesn't matter if they don't develop anything for 3 years; after their break, they look at a piece of code / framework / technology, understand what it does, and continue programming.
And the traits that make you a good programmer help you in other fields, even management. Yes, large corporations have structures, but we need structure to manage them. And we need managers. And a manager who was a distinguished developer will be much better suited for leading a team of developers -- even if he doesn't program any longer. This is a valid career path, and an interesting one at that.
My general opinion is that if you want to stay a programmer, find yourself a role where you can do that. If not, don't bother pursuing programming at all costs. It won't lead you in the right direction.