Pilot lights, flame starts, then burns out

In trying to get our natural gas fireplace to redraft, I\'ve gotten the
pilot to light. Then the fire starts.
After about 2-3 minutes the pilot burns out, which of course shuts the gas
valves and the main
flames eventually burn out. What could be causing the pilot to burn out?

We have a thermocouple/thermopile based natural gas system. Since I\'m
able to start the pilot and
fire, I assume the electrical circuits/switches are fine.

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