Gas water heater won't stay lit

SOURCE: reliance gas water heater 640ycrs pilot light will

if water heater will heat a tank of water before the pilot light goes out you need to replce the gas thermostat

SOURCE: Pilot won't stay lit in Reliance 606 gas water heater

The Reliance 606 has an enclosed thermal couple. Before you try taking that assembly apart take a wire brush to the bottom opening directly under the burner. There is a metal filter on the very bottom of the water heater. It could be that the filter has gotten filled with dust or animal hair. It took a serviceman 2 days to figure this out for me. The water heater has to have good airflow through that filter to work well.

SOURCE: I have a reliance 805pv

OK, make sure your ON-Pilot-OFF knob is turned to "ON" after you light the pilot. Then make sure the temperature dial is not set at vacation setting. It should be set to atleast mid range between low and high at the "A" or triangle symbol, depending on what dial you have. It will take 20-30 minutes for the water to get hot, but the burner should come on right away after it has been relit. If not, you may have to call your local gas co to look at it. Douglas

SOURCE: I have a Reliance water heater - 40 gal Model

In my first 15 years as a plumber I never saw a pilot light issue on a gas WH that a new thermocouple didn't fix. Since the government mandated a redesign of the fire box, I've seen three that nothing ever fixed - two Whirlpools and one (my usually ultrareliable) AO Smith - including replacing the entire burner assembly and the regulator. And I've heard of many others.

Check the thermocouple connection for tight. (Don't strip.. threaded soft metals.)
Check the microvents on the bottom ? of the burn box for dust, even if it is new.
Call Reliant and demand new units until you get one that works.
Try another model. Consider a 52gal electric.

I've always recommended gas over electric, and AO Smith and Rheem were my recommendations (and "Reliants" were "lumber yard" water heaters. Sorry.)

Since the mandated redesigns, I don't really have a "proven reliable" model to suggest. I increasingly believe the restricted air flow design is the ultimate culprit, including any changes to the thermocouple/regulator construct to accommodate the restricted air flow design. Just my hunch.

Offered for what its worth. -- plumber in Indiana.

SOURCE: I can light the pilot and the burner will come on,

Most gas water heater problems can be solved by having service technician perform yearly maintenance. Or by doing maintenance yourself.
This maintenance includes cleaning burner parts and combustion chamber, checking gas pressure and supply, bleeding air out of gas line, checking vent draft, making sure air supply is adequate and not exposed to chemicals, cleaning air intake. Also adjusting flame sensor so it is positioned correctly. If water heater is connected to electric circuit, the outlet must have correct polarity.

You can get gas to appliance indicates the gas control valve and water heater are not locked out. But the gas control valve thermostat can still be bad.

Open following link for illustrations, typical service manuals, and maintenance information, and images of gas control valve thermostats.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot