I don't believe the peak is comparable to professional atheletes, or any other profession that involves intense use of a finely tuned, highly functional body (dancers, for example). In those professions, injuries to the body may not fully heal, and age has a tested correlation to the body's ability to recover and heal. As time progresses, function diminishes. There's statistical outliers, but I'd say these are a rare few with a gift for not injuring themselves, and a lucky biological capability to heal well.
I do think, however, that there is a potential for damage to the mind in programmers. First, there's the once burned twice as shy effect - when a developer has gotten thoroughly hosed by an implementation/design decision, they are less likely to make the same mistake twice, but they are also less likely to reconsider the same solution -- even when the surrounding problem is different. If enough burned patches impact the developer, I could see someone getting caught in stasis, where all they see is the negative and they are unwilling to take risks. Since every choice has potential risk, it can leave a person afraid to do anything at all. I'd say some corporate cultures can cause or prevent this type of burnout.
Second there's the demotivation of working in certain environments. If it's clear that writing good code takes a backseat to writing code in the correct mindless process, it's pretty easy to burn out developers. I'd guess there's a 50/50 chance that the developer leaves to find a better place to work, vs. gives up completely and either stops trying to write good code, or stops writing code all together.
The first burnout scenario is something I'd expect to see after 15 years in corporate world... but mileage varies depending on the company and team. And the amount of beating that occurs when a wrong choice is made.
The second burnout could happen at any age. It might even be worse for those in their first professional job, since they don't have anything to compare to. I know when I entered the workforce in 1998, within 5 years, half of my fellow software engineer friends from school had quit to become massage therapists. After the 5 year mark, most of collegues have stayed in the business, they just shift teams and companies when they don't like the scenario.
But I don't think either burnout is inevitable. The key is realizing the signs in yourself, and finding a way to change the situation so you still enjoy the work.