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The GPU showed random failures so it was replaced. The machine was stress tested overnight (connected to a charger) and worked smoothly.
When running on battery it experienced random restarts and the error above. That is the only error ASD shows.
C9560 is measured at 1.55V (should it be measured at 1.8V?).
AN UPDATE:
I've also noticed that Q5503 was not attached properly - now ASD shows no errors BUT the machine still goes into sudden sleep mode.
GPU was never bad and C9560 still needs to be replaced! Let ASD loop to see if it catches an error. Disconnect battery indicator to rule out a bad lid sensor.
C9560 worked again temporarily after you heated it. It is close to the GPU so it gets heat in the BGA rework process whether indirect from top heater or from bottom IR. When it returns to its initial state, it'll crash again. Replace it with a non-tantalum.