Water Heaters - Water Heater shuts down completely

Hello, I have tried to find the solution in this forum to my issue here at hand and could not find it, so i am hoping that you will be able to put me in the right direction.

The water heater is a Kenmore, model #153.336401HA.
Issue description:
No hot water. Took a look at the pilot and it was out. I sucessfully re-lit the pilot light and the water heater immedately started to heat (main burner lit)...

After about 10 minutes of heating I hear it kick off..while it was heating.. I knew it wasn't on long enough to re-heat the whole tank, so I knew something was up. I went and checked for the pilot light again and it was out. Not sure what's going on here.

Do I have a faulty C02 sensor? I just want to make it clear that it is not the pilot light that goes out, the water heater is in the heating stage when it shuts down.

Any help would be appreciated!

Thanks.

I thought I would post a reply to my own question now that I have the problem solved..at least temporarily.

It turns out that the thermocouple was giving a faulty reading and shutting off the gas supply. I learned a little trick to try before replacing the thermocouple. I lightly sanded the tip of the thermocouple with some 300g sandpaper, cleaning off all the crud, and the system is still working correctly as of 2 days later. I am only suggesting this solution to get by for a couple of days. I have a thermocouple on order..

Yes, my first thought was a thermocouple. They eventually get bad enough the pilot won't stay lit after holding down the bypass button.

Never thought of cleaning it off to get you over the hump temporarily. Thanks for the tip.