Water Heaters - Whirlpool Nat. Gas water heater

I replaced my old water heater in Dec. 2007 with a Whirlpool 50 gallon N.G. heater. It worked fine until 2 days ago. The pilot light won't stay lit. I can only get the pilot to light intermittently and the burner lights just enough to avoid cold showers. Once the burner kicks off the pilot light goes out with it. I replaced the thermocouple and it lit, and the burner lit and heated only to the warm setting on the thermostat (I had it cranked to the hottest setting). Once the burner goes off repeated attempts to relight the pilot are futile. The pilot lights but when I let pressure off of the pilot button it goes out. Any suggestions? Water heater model # BFG1H5040T3NOV

Is the flame hitting the thermocouple properly? Good solid flame hitting about 2/3 up on the thermocouple.
Is the copper line or wire connected and tight. If loose it will cause pilot failure.
How does the pilot flame look?

Here is a great link. Click on the troubleshooting flowchart and it will walk you right through.


http://www.whirlpoolwaterheaters.com

Click on troubleshooting guides,
Scroll Product type - Click Flame Lock
Click Chose product type button
Click View FVIR troubleshooting flowchart

I honestly believe that it is a thermostat problem. I tried to light it before my shower and it wouldn't light. I took a shower anyway and had hot water. Once I was done I turned the control to a lower setting and the thermostat "clicked" near the lowest setting, I was able to get it re-lit. My theory is that the thermostat is stuck at a certain temperature and once the temp of the water gets below that point then it will light. It will not light if the water temp is above the point that the thermostat is "stuck". In response to the earlier reply, I seated the thermocouple all the way into the holder and the flame does cover at least 2/3 of the sensor.