Wonderful interlude in troubleshooting.

Me: "The problem is asynchronous network IO. That's when the server is putting stuff out there and cheerfully waiting for a response before it continues. It's supposed to wait, but not this long, so something has to be going wrong, possibly at the network level."

SomeoneElse: "Can someone translate that from SQL Engineer to English?"

Dan (who has clearly seen Cool Hand Luke):"What we have here is a failure to communicate... between SQL and the app server."