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Thanks for reaching out!
Are you using the Edison to power your camera? You mentioned that you are using an external power supply, is this power supply powerful enough to power both the Edison and the camera at the same time? A lack of power when trying to power the camera could be the reason why the board keeps rebooting.
If the power supply is powerful enough (I'd suggest 2A at least) or if you are not even connecting the camera when this happens, then the issue might be due to an issue with the image installed on your board. If that were the case, I'd suggest you to reflash the board with the latest image using the flashall method (https://communities.intel.com/docs/DOC-25154).
I hope this information helps you,