An oscillating magnetic field of decreasing amplitude causes the magnetization to continually reverse and remagnetize. Since the amplitude is decreasing the last low amplitude field yields the final state of near zero magnetization. For simple steel and some stainless steels the coercivity is quite low and so the amplitude does not have to be very large to cause the demagnetization. In audio tape recording, this process is call de-gaussing. The recording process, where a DC field is applied while the oscillating field amplitude decreases, is called anhysteretic recording. The result in magnetic tape is that the final resulting magnetization along the tape is the determined by the DC field magnetitude.
Sometimes you want to magnetize a screw driver and you make this by stroking a magnet along the tip. (Sort of an anhysteretic recording process) However, after some extended use of the screw driver you find that it is no longer magnetized. This is because stresses of use causes this magnetize state to relax to become demagnetized. You can also just repeatedly tap the screw driver tip to induce this stress and this will also cause demagnetization to occur. You might find that the vernier calipers tips will also demagnetize if you tap them a lot! But, maybe you do not want the tips of your calipers to look like the ends of your screw drivers!