For Beta sites, it is not uncommon to get closed if they for example don't fullfill the desired activity criteria as explained in Stack Exchange blog post When a Site Grows Quiet (2012-04-24).
My question is, can something like this happen to graduated Stack Exchange sites too, if for example their activity drops too much or does not grow fast enough?
Are there other criteria or conditions that would make a graduated Stack Exchange site closable? If so, what are such close reasons? The only things apart from the (lack of) activity, which spontaneously comes to my mind, that could kick a graduated site out of its comfortable stable equilibrium is a drop in the quality of the content in the course of time, or that the site can no longer fulfill its mission as often stated in the "About" for some reason. But maybe there are other things I am not able to think of...
If a graduated site is getting into serious problems, would Stack Exchange give them some timely warnings, such that people would have a fair chance of trying to solve the issues and avoid the site getting closed?
Did something like this ever happen in the past?