Personally I think it would be better to turn it off and on each time. I think that the electronics wear out more when the instrument is turned on than when it's not.
For PSR-3000 owners (like myself): don't keep it turned on too long without playing it, it's not too good for the display. Mine loses its brightness after a while. When I turn it off for a while, it's back to normal, but I don't think that it's very good for the display.