I confirm this issue.
For the purposes of this experiment, I replaced the power supply with a similar one equipped with an LED. The power supply is connected to an electrostatic precipitator equipped with a power button.
We turn on the electrostatic precipitator using the button. The power supply LED lights up. The Odroid M1 turns on and boots normally.
We shut down the Odroid M1. We turn off the electrostatic precipitator using the button. After 2 seconds, we turn it back on.
The Odroid M1 does NOT turn on again. Therefore, replacing the power supply did NOT solve the problem.
Experimentally, we have determined that the Odroid M1 does NOT turn on again as long as the power supply LED remains lit, even when the electrostatic precipitator is turned off. Therefore, the issue lies with the residual charge in the power supply capacitors.
If, with the electrostatic precipitator turned off, we wait until the power supply capacitors are depleted and the power supply LED goes out, then when we turn on the electrostatic precipitator again, the Odroid M1 turns on normally and boots normally.
Meanwhile, the Raspberry Pi doesn't have this power supply issue.
Therefore, this is a design flaw in the Odroid M1.