Given the scenario reported above, I rather think that an Explanation 3 is possible and seems to fit all the facts:
Due to the high rate of descent and distance between the a/c when the TCAS Resolution Advisory was issued, the TCAS had calculated that the best manouevre was for the 737 was to continue descent to avoid conflict. Coincidentally, the altitude capture mode was entered at this time (F227), which required a reduced rate of descent to level at F220. This was dutifully followed by the autopilot. Immediately following the autopilots reduction in rate of descent, the 737 pilot disengaged the autopilot (F225) in accordance with TCAS procedures and attempted to follow the “descend, descend, descend” order. However, because the rate of descent had been reduced by the autopilot following the alt capture mode the TCAS now recalculated that the new best manouevre to avoid conflict would be a reversal, “climb, climb now”.
I surmise that:
1. What the pilots reported was accurate.
2. TCAS did initially issued a descend RA order.
3. The rate of descent was reduced by the autopilot during level off, before the pilot had a chance to respond to the RA.
4. The pilot disconnected the autopilot and attempted to follow the descend RA.
5. Because of the reduced rate of descent, the TCAS recalculated and issued a climb reversal RA, Climb, Climb Now”.
6. There was no failure of the TCAS equipment.
The initial RA given by TCAS is a known problem when climbing or descending at high rates close to level off with traffic occupying an adjacent level. We usually accommodate this by reducing the climb/descent rate approaching level off if there is known traffic. Known traffic may be seen on the TCAS display (if the signal is not blocked) or by advice from ATC. Just my two bob’s worth.