Thanks for all your responses.
The doomed Airbus issued 24 automatic messages during its final messages, each adding to a sense of urgency and indicating the unprecedented distress of the aircraft. Airspeed indications were incoherent, and system after system was failing.
Query: If such signals were received "live" by radio, why, on Earth, couldn't the aircraft have radioed its exact position as well? I do realize that, despite all our advances, this aircraft might not have had GPS equipment aboard (although this seems hard to believe), but the inertial guidance information it had relied upon should still be available, at least on a "last known" basis.
Further, the requirement to store inflight data in black boxes from a purely technological standpoint seems obsolete, as I've heard from at least one source.