Most modern subs have an auto-sensing circuit built in so after a few minutes with no signal they will go into standby mode. While this isn't exactly "off", it should be close enough.
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I agree with both of the above replies... leaving a self powered sub on all the time is completely fine. Both my REL Stadiums have been, [aside from a few severe storms or hurricanes when turned off for precautionary reasons only], left on for the past 10+ years and have been trouble free and perfectly performing. FWIW my entire predominantly tube based system does too... Not only does it sound better but it saves each component from those relatively gruelling turn on procedures.. that is pressing the power switch, yikes!!!! (No, I'm NOT being facetious).