1991 RELIANCE MODEL 501, THE PILOT LIGHT WILL NOT STAY LIT.

SOURCE: need to empty reliance 501 hot water heater how?

1) Shut the breaker off to it at the panel. 2) Hook a hose up to it (the bottom has a drain). 3) Close the valve to the water heater (on the cold water supply). 4) Open drain on the bottom of water heater. 5) Open the relief valve to allow air into the tank (it won't drain otherwise - think if you put your finger on one end of a straw - the liquid stays in until you let go). Why are you draining it by the way?

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: The pilot light went out

The paid answerers might have a specialist in your model of water heater.
As a free answerer, I specialize in providing resources that might help you for free.
When you say the gas control pieces, I assume you mean you replaced your entire gas valve with a generic dial-type gas valve.
You replaced thermocouple, but you did not replace burner assembly that includes the pilot tube.
Your other gas appliances are working fine.
You have not installed a new gas furnace with a blower that is vented up the same chimney as the water heater.
You have put your hand near the vent hood to see if there is backflow coming into the water heater when the furnace turns on.
You have removed the vent hood to give you access to the vent pipe, and you lit a match and the smoke from that match drafted upwards. You have done the lighted-match test when the furnace turns on which reveals the general condition of the venting stack.
You have checked your outdoor vent stack to make sure there is no obstruction, or the vent hood is not missing.
The burner flame on the water heater is a clear blue color with very little yellow. This shows the quality of the combustion air and reveals if amount of gas flowing to burner is restricted.

http://www.thetankatwaterheaterrescue.com/forums/forum3/

http://www.reliancewaterheaters.com/prod/gas.html
Reliance is an AO Smith company
The site doesn't have a manual for the 501
I e-mailed Reliance several weeks ago asking for a 501 manual.
They send a generic gas water heater manual with no troubleshooting

http://www.reliancewaterheaters.com/lit/om/g616.html
Link above shows a typical Reliant heater, the 616
Age of your water heater can be seen on serial number.
The two numbers following first letter are the year water heater was made.

http://www.reliancewaterheaters.com/lit/om/manuals/186486-002.pdf
Troubleshooting begins on pg 29
Troubleshoot flowchart begins on page 31
The new gas water heaters have the FVIR system so troubleshooting includes that information.
I don't think the 501 would have a FVIR flammable vapor prevention because it is older
The new systems have an igniter
The troubleshoot flowchart gives valuable information

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: Our 40 Gallon Reliance 501

Many problems are solved by replacing thermocouple, but usually pilot will not light if thermocouple is bad. And some Reliance water heaters, the thermocouple is grouped with TCO and not generic part from hardware store.
If the combustion chamber is sealed with gasket, you might need spare gasket on hand before taking out the burner assembly to replace thermocouple.
http://www.youtube.com/watch?v=v0aBPsNg6vo

Gas water heaters can malfunction for many reasons.
Service tech is best resource unless you have manual and can take time learning parts and how to replace.

Gas water heaters require periodic cleaning of combustion parts and tubes.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

Other ez problems include:
Gas shut off valve not fully open and handle is not parallel with gas line, so gas is partially shut off
If water heater flooded, then replace heater.
Excess water vapor from bad venting rusted out the burner parts. Inspect burner for rust.
Not enough combustion air, for example the house was recently weather-tightened, or a louvered door replaced with solid door. Or air intake screen located on bottom of heater is clogged with lint or dust.
Very hot attic can cause pilot to go out.

Trace amounts of pool chemical, laundry chemical, process chemicals, wax, etc can cause damage to burner parts.
Low gas pressure can cause problem.
Air in the gas line.

Bad gas control valve.
If ECO was tripped, there should be no gas to pilot.
Gas control valve might have debris or water from gas line.

If FVIR event tripped FV sensor, that would explain problem, and you would need service technician.

If repairs cost more than $330, then buy and install new water heater yourself, same day.
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Upvote the help.
And take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Testimonial: "Thank you for your response. We ended up cleaning the burner parts the best we could and flushing the tank. Whatever it was it worked! Thx again."