This is what Wikipedia says about this: "High turnover may be harmful to a company's productivity if skilled workers are often leaving, and the worker population contains a high percentage of novices." I agree. However, I believe that low turnover may also be very harmful.
I've found this good article where John Sullivan explains why low turnover could be a troubling symptom. It's a really good read, but rather generic. It is not specifically about software teams. My experience is mostly focused on programmers and their turnover. I've learned that low turnover negatively affects code maintainability and encourages hero-driven development and strong code ownership (both of which are bad practices).
"Turnover" is basically the act of replacing an employee with a new employee for any reason, including termination, retirement, resignation, or any other. Simply put, the more people your team loses every year, the higher your turnover. If there are 20 programmers on your team, and five of them walk away every year, your turnover is 25 percent.
I can't pinpoint what number you should aim for, but I strongly believe that if you consider programmers to be a valuable long-term asset, and try to retain them at all cost, you're doing it wrong.
My point is that a healthy software team must replace programmers regularly. I would say having one person on board for longer than a year is asking for trouble.
By replacing, I don't necessarily mean firing. Not at all. I mean moving them away from the code base. Obviously, if you have a single code base, replacing will mean firing.
When programmers stay together for a long time, working on the same code base, they inevitably become subject matter experts. First of all, this leads to strong code ownership. Naturally, each of them becomes a specialist in his or her own part of the code, mostly because it's easier to work with something you're familiar with instead of jumping from module to module. Needless to say, strong code ownership is a bad practice. Collective code ownership is a much better alternative, as explained by Martin Fowler.
Then, having strong experts on the team inevitably leads to hero-driven development, where firefighting is very much appreciated. An expert doesn't want to lose his or her position, and always tries to demonstrate how valuable he or she is for the team. The best way to do this is to solve a problem that nobody else can solve. That's how one gets "job security". And that's how the team starts to degrade. This blog post by Fredrik Rubensson is right about this problem.
Thus, to achieve higher maintainability of the source code and robustness of the product, we must rotate programmers, preventing them from becoming subject matter experts.
I realize this idea sounds counterintuitive, but think about it. By keeping people together, working on the same problem for a long time, we put a lot of knowledge into their heads, not our source code. These people become the asset. They become smarter, they know the solution very well, and they solve all issues rather quickly. But the code base degrades.
When the time comes to change someone (for any reason), the loss will be damaging. We may lose significant knowledge, and the code base left behind will be unmaintainable. In most cases, we will have to re-write it. That's why in most software teams, management is afraid of programmers. They are scared to lose key software developers, because the consequences may be fatal.
In the end, programmers control management, not the other way around.
It's Not a School! — This earlier post explains how this problem can be solved without firing or rotating programmers, but few teams, especially colocated ones, can afford it. If your team can't, just try to keep your turnover high enough to prevent the appearance of heros (a.k.a. subject matter experts).