As a simple-minded Twotter driver there is one factor here which seems critical to me. If the stall warning sounds I know to get the nose down in a hurry then grab for the apehangers to add power.
In this case, the first question that needs to be answered is why the PF decided to pull the nose up when the aircraft was in otherwise stable flight at the time the autopilot disconnected. That might explain the mindset that had to be overcome to get things under control again.
In this case the stall warning only sounded (twice?) briefly which was probably the critical misleading clue which convinced the crew that they were not stalled.
While the report isn't perfectly clear, the way I read it, the stall warning sounded at least three times: Twice immediately after the PF initially pulled the nose up, while they were in the steep climb, and once after the climb peaked and the aircraft regained airspeed as it began to fall. The report says the aircraft was stalled for the remainder of the flight, so I suspect the stall warning was sounding continuously thereafter.
The PF reacted to the first stall warnings by trying to lower the nose during the climb, but then later applied TOGA power and pulled back before they had recovered. At some point near the top of the climb, he dropped the throttles to idle, but still maintained the nose-up input.
As they started to fall, he again tried putting the nose down, but when the speed picked up, and the stall warning sounded again, returned to full nose-up input, which he retained to the end, even though the attitude was something like +15 degrees, and the AOA+35 degrees. By then, the speed sensors were working again, so all his instruments should have been working as well.
If the stall warning had behaved as expected by any sane pilot and sounded continually during the stall then any sane pilot would have realised that the aircraft was indeed stalled and applied the correct recovery.
That's a good question, which brings me back to what the PF's midset was, and why he didn't react correctly to the stall warning in the last 2 1/2 minutes of the flight, even though the warning must have been sounding continuously. That should have been enough time to reconsider what he was doing, and try something different.
Why the hell did the stupid automation silence the stall horn ?
THIS SHOULD NOT HAPPEN
From the BEA news release:
"When the measured speeds are below 60 kt, the measured angle of attack values are considered invalid and are not taken into account by the systems. When they are below 30 kt, the speed values themselves are considered invalid."
Perhaps they consider the instrumentation to be unreliable at those low speeds? The lack of wind noise past the cockpit should have been a clue that they weren't making much headway.
Even if they didn't suppress the alarm when the speed dropped, would it have sounded when the AOA, which is the primary input, dropped to only 4 degrees, as it did near the top of their climb?