In my experience, that is not a typical result for that type of connection. I've had two different receivers and two different subs connected like that, and the auto-off worked in both cases. In fact, my experience is that the subs will shut off whenever there are long pauses without bass while watching TV or a movie (with one remedy being to increase the output level on the receiver for the sub signal).
When you say that the sub never turns off, I'm guessing that it has an LED that is indicating that it is powered?