Water heater pilot light won't stay lit - thermocouple replaced

My 6+ year-old water heater's pilot light won't stay lit. I held down the pilot light switch upwards of 5 minutes and it still extinguishes when I let go. The flame encompasses the last 2-3 mm of the thermocouple so it's positioned correctly. I put in a new thermocouple and same problem.
How likely is it that the new thermocouple is bad?
How likely is it that the control unit is bad? If the control unit is bad, should I just replace it or replace the whole water heater?
Thanks!
Getting cold in Austin ...
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Tai wrote:

Try another T/C (only couple bucks). Don't install the T/C, leave it hanging outside the heater where you can put a small torch flame to it. See if the valve will hold in. If not, the control is bad. The cost of a new control is quite high, maybe $50-100. On a 6 yr old heater it may not be worth fixing.
Jim
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