It is hard to understand why pilots would continue pulling back on the stick when the stall warning was going off; almost the first lesson in flying is to lower the nose when the stall warning sounds. However, it’s possible they didn’t trust the stall warning. They may have thought it was a false alarm.
When the pitot tube is blocked, the airspeed indicator starts acting like an altimeter; the higher the aircraft goes, the faster the airspeed reads; in reality the opposite is happening. The aircraft is slowing, and will stall if the nose isn’t lowered.
They were flying in bad weather at night, so probably had no visual reference outside the cockpit and had to rely solely on instruments. The way out of the problem is to fly pitch and power; use the artificial horizon to level the wings and keep the nose down, and a power setting known to give a safe airspeed.
I have to believe that the pilots were fooled by the avionics to think the situation was different than what it actually was.
“When the pitot tube is blocked, the airspeed indicator starts acting like an altimeter; the higher the aircraft goes, the faster the airspeed reads; in reality the opposite is happening. The aircraft is slowing, and will stall if the nose isn’t lowered.”
When the front of the pitot tube is blocked, the airspeed reads zero. When the entire pitot tube is iced over (both the front and the drain hole), then the airspeed acts like an altimeter and increases in a climb and decreases in a descent.
As the airspeed approached zero, the warnings would stop. The logic or illogic in the software was that the speed was invalid. Combine that with poorly trained pilots with almost no experience actually flying an airplane in a difficult situation.