Can you see the pilot flame ? it should be bright blue and fully engulf the tip of the thermocouple , if there is one .
Does your power vented water heater have a flame sensor , in addition to the thermocouple ?
If you inspect the connections between the burner and pilot assembly ( hidden in the bottom of the unit ) and the gas valve , you may see a thin wire , in addition to the pilot line ( 1/4 " dia aluminum tube ) , the main gas line to burner ( 1/2" dia aluminum tube ) , and the thermocouple ( 1/8 " dia copper solid wire ).
If so , the wire is for a flame sensor , which must be cleaned occasionally , by gently sanding the probe , located at the burner .Note - sanding a thermocouple does no good , they're cheap and easy to replace . A thermocouple creates electricity , approx 250 millivolts , by being engulfed in the pilot flame . A flame sensor conducts electricity when engulfed in flame , thereby proving that the flame is lit.
To clean the flame sensor , and/or replace the thermocouple ( might as well while you're in there ):
1) shut off gas to appliance . We don't want to read about you in the paper tomorrow .
2) disconnect all outputs from bottom of gas valve ( flare fitting for main and pilot lines , thermocouple , sensor wire , etc.)
3) remove burner from bottom of water heater
4) clean sensor , replace thermocouple
5)re-assembly is reverse- ensure burner is properly placed - scope it out with a flashlight as you reinsert burner , there's probably tabs to locate it.
6) turn on gas , relight burner and test all joints with soapy liquid for leaks .
As a licenced gas fitter , this would take me about 1/2 hour to do , and I'd charge $80.00 plus travel
Naturally , you accept full responsibility for your actions , if unsure , call a qualified technician .