But it seems to have been up (for whatever reason) and stayed up. Has the BEA explained why?
The reason is simple. The pilot's nose-down inputs only reduced the elevator deflection a little - the elevator still stayed "up".
He didn't keep the stick forward far enough or long enough to move the elevator back to neutral, and then into the "down" position. The THS would only have started moving "down" again once the elevators were pushed beyond neutral.
The THS behaved exactly as designed.