You need to recharge at night like an electrical car. I guess
solar power is somewhat ruled out,
and so is
fuel-powered hearts. Maybe nuclear power would work, though I'm not so sure that's 100% safe either :)
Second, when doing exercise, etc, you need to manually turn up the pumping speed. I'm sure someone could develop an adrenaline sensor.
Third, a mechanical heart is pumping blood with constant speed. So, your blood pressure would not be, say 120/70, but more 90/90.