The problem with any microcontroller is that they will go into a reboot loop when the supply voltage is near their low recommended operating level. This can also occur when the voltage supply is ok but the current supplied is insufficient to supply the booting process. This is most likely what is happening here. So the device can't monitor itself under those conditions since it can't fully boot.
An external voltage watchdog (chip) will hold the RESET of the device until the supply voltage reaches a preset level, which in most cases indicates a safe booting condition.
If I recall, the STM32F205 in the Photon has a brownout detector but I'm not sure how this would work here. If enabled, it could prevent the processor from doing the boot loop. Research required.
UPDATE:
You may want to look at this thread (with caution)...