There's a problem in the server software. When the load gets high, it fails catastrophically instead of gradually. Robert and Patrick Collison are investigating, but they're still not sure what the problem is. My guess from the external evidence is that it's related to garbage collection.
Killing the server process fixes the problem, at least for a day or two.
I'm assuming it's traffic-related, because I've run had ASV running on my server for weeks on end without real issue (I don't get much in the way of traffic).
Killing the server process fixes the problem, at least for a day or two.