Of course, if something goes right the first time, it means that there is something wrong with it! Turns out it's nothing wrong with ours. The carefully designed power-up circuit only does half of its job: turn-on is OK, turn-off is not. Oscilloscope and multimeter diagnosis show that the levels at the comparator pins are correct: when I push the button the voltage rises above the reference voltage created by the voltage divider.

We suspect something else... We turn off the circuit by pulling down the EN pin of the LDO with the MCU. But the MCU's pins operate as long as it has a stable power supply. When the 3.3V drop. the pin becomes High-Z.

The NCP705 has the Enable falling threshold at 0.4V. So the MCU releases the EN pin way before the 3.3V rail collapses and the divider with the diode keep the part alive.

We'll think about that...