Another scenario is if I boot the Omega2 up with the battery attached and using USB power and then disconnect the USB power, the Omega2 continues to operate. But... if I re-attach USB power again, the Omega2 dies (and the orange LED goes off and the AP stops to work). Power LED is still on and if I have anything presented on the attached OLED expansion, it still shows even if the Omega2 is not working so the hardware stack has power coming into it.
Fairly common problem I've seen. What I do to overcome it is use a really good power supply (>=2A) and a short USB cable with thick gauge cable.
Typically I see it when powering the device via USB with battery attached and then there's a power failure. The device continues to run on battery, but as soon as the power returns, it dies. Solution = short, thick gauge USB power cable.