I don't know. I wonder what sort of dormancy features these things have. Most stages of the life cycle, if not all are host associated. Once the host is gone the mites die rapidly. There probably are some weather related exceptions, e.g. rapid and low temperture freezes. I'll see if I can find some info on the survival rates absent a warm host. I'm guessing hours too days.
There are a number of "incomplete" hosts; man for example. Humans with intact immune systems can harbor the mites but APPEAR to inhibit completetion of the reproductive cycle. Therfore, in healthy man, infestation is only a locatized and limited disease. In immunocompromised individuals sarcoptic mite infestations have resulted in death. My point being if there was a warm mamalian body around the den to "provide shelter" so to speak the mites my survive much too somewhat longer.