The telegraph has some more information on what caused the last partial ping:
Likening the sequence to a car spluttering as it runs out of fuel, Mr McLaughlin told The Telegraph: "The partial handshake would be the plane running out of fuel and faltering for a moment, so the system went off network and then briefly powered up and had communication with the network. The plane looked for a final communication before it went off – and that was it."
MH370 missing plane: 'black box pings' tracked to same point as final 'half-handshake' - Telegraph