The accelerometers in the IVSI sense acceleration in the aircraft vertical only. As you enter a turn you have to increase lift to account for the portion of lift now acting towards the centre of the turn; an acceleration in the vertical plane.
By 'normal' acceleration, I assume you mean an increase in speed? Which is an acceleration along the longitudinal axis, the accelerometers in the IVSI aren't aligned to sense on this axis, so no climb/descent is displayed.
As for why only above 40 degrees of bank, I can only guess that maybe the instrument is calibrated for the smaller bank angles used in normal flight.