I didn't see anything in the literature that suggests it will turn itself off. I saw some that advertised the feature and probably assumed any of the better mice would do the same. They actually say that removing the plug from the USB port and clicking it into the body will prolong battery life. There really is a switch; it's just tucked inside the USB cavity, and can't be conviently tripped without the thingambob.
Remember the old story about "If cars were computers?" Your car would get 500 miles per gallon, zero to sixty in under four seconds, with a top speed approaching supersonic. If it were made by MicroSoft, it would also get hijacked every twenty miles, require a keyboard command to turn a corner, and crash three times a month. Now we discover that if we want to shut off the engine, we've got to pop the hood and pull the ignition wire.
Thanks for the answer. This is a MicroSoft 5000, if it makes any difference to anyone.