When the aircraft got very slow, i.e. less than 40kts or 60 kts (if I remember rightly), the stall warnings ceased. Airbus has programed it to do that because at that speed you will be on the ground, according to them. (it seems that they never considered that an aircraft would get that slow in the air)
On the one or two occasions that the pilot flying relaxed the back pressure the airspeed increased (the pitot problem had rectified itself by then) & the stall warnings started again. This caused some confusion & lead the pilot flying to reintroduce full back stick.