I think that you are probably drawing too much current from your 3.3V supply (Are you using the 3.3V from your serial/USB converter?). This is causing a reboot once it hits a particular point where additional current is needed, and resets itself. If you solder on the 3.3V regulator included with the bare PCB you can use the 5V directly from the USB/serial converter instead of overloading its on-board converter. There are two places that accept 5V on the Di board: on the end of the board labeled UART, and at the opposite end marked USB (They are connected together so it doesn’t matter which you use). I haven’t had any stability issues powering the Di that way, and I’ve connected a USB flash drive to the USB GND, 5V, and D-/D+ pins successfully.
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