Of course, there are no absolutes. But how common are projects like that? Exceedingly rare in my experience. The great majority of projects (especially web and tech) are no longer profitable or decreasing majorly by the time of sell. That's been my personal experience from extensive study and searching for profitable projects for sale. But one could always get lucky I suppose.
It's common. As soon as your project starts making money it also starts giving you anxiety and stress. Having a project that's stuck on a moderate income is a curse and you dream of getting rid of it. Been there many times and I've also closed down a lot of profitable projects even without selling them. That's how much of a burden it is. The fun part is creating something new before it starts getting paying users.