Weebobby:
There was something that led them to that spot in the Indian Ocean, some clue or intelligence that meant Ocean Shield heard the first pings on the very day the black box batteries were due to start weakening. Something told them to look there... I doubt we will ever find out!
It was the realisation that the aircraft was flying lower.
The resulting faster IAS, slower TAS, and thus slower groundspeed - and the resulting shorter range - meant that the search location had to move along the last ping-ring towards the northeast. Simple, really.
What we don't yet know, is why they suddenly realised that the aircraft flew at low-level.
P.S. If someone can post the fuel-burn/altitude tables for 1,000' and 10,000', it would be fairly easy to calculate roughly how low it flew.