For example Valve can pull this off, they are a game company, always building the next great game, they always have something new to work on and have gone to great lengths to keep their employees involved and attract top talent. They have avoided stagnation.
On the other hand, many of the companies you see get acquired built one or two focused products, they don't have 'the next big game' to work on, that is boring for many people, particularly the 'founder type'. Boredom -> stagnation -> erosion.
You could say that company X could just define themselves as e.g. a 'mobile app' company the way that Valve is a 'game company', but in reality, 'mobile app' is way too broad. How is a 'mobile app' company any different than startup? The difference is that instead of investors taking the risk on the new product, the company takes the risk, which doesn't bode well for the constant year over year profit ideal.
The 'company taking the risk' model can work, e.g. Google, but you have to be wildly profitable to pull it off, that is hard, really hard, so hard that only a hand full of companies have ever pulled it off.
tl;dr Privately held long term companies can get boring quickly. It takes a very particular type of market, a founder who really wants a lifestyle company, or a company that is wildly profitable to avoid stagnation. All three options are relatively rare.
