If you find any supporting data, I'd love to see it because I dearly hope this to be true.

Unfortunately, I suspect most of these businesses are vulnerable to larger competitors, market fluctuations and other risk factors that one would want a growing business to protect against.

However I'm sure many businesses have managed to keep things fairly stable with modest growth and loyal customers for the lifespan of their owners relationship with the business. I'm just not sure if that is enough to support the fact that there is in fact a state of equilibrium for a business.