What's most interesting in this case is that the systems warned the pilots of an impending stall, but then once they were in a stall, there was no warning at all, as if they had recovered from the stall. That's really unfortunate.
That's because once the airspeed drops below 60 knots, the input from the angle of attack vane is ignored by the flight computer. The computed angle of attack is how the flight computer determines the airplane is approaching a stall, so without a valid input from the AOA vane, the computer can't sound the stall warning. The AOA vane is just a triangle-shaped piece of metal sticking off the side of the airplane on a little lever, so the airflow naturally positions it, just like a weather vane. As the angle of attack changes, the vane moves, providing an input to the computer. Below about 60 knots, though, there isn't enough airflow to move the AOA vane to a reliable, steady position, so the information is discarded by the computer.
In this case, you're right, it was unfortunate because it provided a confusing result to the crew. They had pulled the airplane's nose up into a stall, and when the airspeed dropped below 60 knots, the stall warning stopped. At one point, the crew did lower the nose of the airplane, which caused an increase of airspeed, which is of course precisely what they needed, but as the airspeed increased beyond 60 knots, the stall warning suddenly started back up. That made them think that what they were doing was making the situation worse, not better, when in fact they were doing the right thing. They pulled the nose back up and then never got it back down until they hit the water. Even when valid, the AOA vane never indicated an angle of attack of less than 35 degrees - generally speaking, almost any general or commercial aviation wing will be well into a stall by about 15 or 16 degrees AOA.