Cutting a long story short, as soon as he signed off from one ATC area, he promptly turned off all his tracking devices (so from then on only military primary radar could track him, not the secondary radar used by most ATCs), then changed altitude and sneakily doubled back on himself, very cunningly flying a flight path that sneaked him under and past all the nearby primary radars, seriously minimising his chances of being spotted.
(Another reason the electrical failure hypothesis is absolute rubbish, his turnback flight path was far too well-planned.)
By the time the next ATC area (Thailand IIRC) realised that he hadn't checked in with them, he was long gone and heading towards the South Pole for six hours, way out of range of any radar on the planet (except possibly Australian military right near the end).
Had they realised about the double-back earlier they might have got him, but as it was, when he didn't check in they assumed an accident, and started searching where he would be given his last known trajectory, i.e. in the South China Sea.
By the time they reviewed military radar tapes two days later and saw this passing object on the fringes of their scopes, everyone was long dead.