Quote from TURIN:
"Chris Scott.
Temp/Time limits on the APU are due to a rotor bow problem caused by excess heat soak after shutdown.. The quick fix is to leave the APU inlet door open to allow sufficient ventilation of the APU powerplant. Long term fix will be hardware/software changes."
So let's get this right. We have an APU that has to be treated with kid gloves, including 30-minute rest breaks, and currently no on-board battery available to start it. I remember flying a long-haul airplane about forty years ago that was still dependent on a GPU for meaningful electrics on a turnround. It was called a Seven-Oh-Seven.
Right now, its great-great grandchild is looking to be a bit of a dog. Shame.
End of rant...
Your not alone on shaking your head on this one Chris. Of the Boeings that I have flown I have only had a problem once and that was on the 777 when it auto-shutdown due to an internal limit.
Kid gloves is correct--among the systems on an aircraft that should report fit for duty when called upon the APU is certainly in that august group. Having to wet-nurse this thing as Turin describes is not instilling much confidence at the moment...