My gas hot water tank burner wont shut off when not running hot water for very long

Check for error codes and service manual on following link:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

Replace gas control valve
http://waterheatertimer.org/How-to-replace-Honeywell-gas-control-valve.html

Gene:

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What are you expecting to happen?

I assume the water heater and water inside it is cold (otherwise you would not be lighting it). You light the pilot. The main burner comes on and the pilot lights it. The main burner should stay on until the tank is hot, When the tank gets hot the main burner should shut off but the pilot stay on. If you draw hot water, cold water will run in and cool the tank. If yu do nothing the tank will eventually just cools off. then the main burner should come back on to reheat the tank.

Check gas control valve.

Good luck,

Marty

the tank needs flushed out ! heres how. Water heater manufacturers recommend flushing sediment from your storage type water heater periodically.
If your water heater is gas, set the gas valve to "Pilot" to prevent the burners from coming on while you are flushing it. If your heater is electric be sure to turn off the circuit breakers. With an electric water heater, if the water level drops below the heating elements and the thermostat turns the elements on, the heating elements will probably burn out quite rapidly. Connect a garden hose to the drain valve at the bottom of the tank, Close the shut off valve on the cold inlet to the water heater. open the temperature/pressure relief valve at the top of the tank by lifting the lever. Leave the valve open. Open the drain valve at the bottom of the heater allowing the water to flow out through the garden hose. when the water is clear your finished. close pressure relief valve on top of tank and turn water back on.
Open a hot water faucet in your house, and let it run until no air bubbles come out.

Turn the heater back on, and with gas units re-light the pilot light if necessary. good-day !

The igniter is glowing, but no gas ignites?
So either the gas is entering combustion chamber and not lighting because igniter is positioned incorrectly -or- no gas is entering combustion chamber because air in gas line or bad gas control valve thermostat or gas line is clogged.
When you 'restart' the water heater, somehow you are getting gas to the burner and it is igniting.
I'm not sure what the flame switch is. If the ECO was cut out, the gas control valve would not send power to the igniter and there would be no gas available for 'restart.'
I would adjust location of igniter, check if gas is entering combustion chamber, clean the gas line to the burner, and bleed gas line for air, but another suspect could be the gas control valve thermostat.
Identifying numbers are usually on side of gas valve.
Open following link to help identify gas valve:
http://waterheatertimer.org/How-to-adjust-temperature-on-water-heater.html#intelli
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean

Probably the burner and parts need to be cleaned yearly as recommended in most gas water heater manuals. Both tank and tankless today recommend same.
Open following link for Bosch troubleshoot resources:
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html

A leaking water heater cannot be repaired, assuming it's the tank leaking and not nearby water pipe.
http://waterheatertimer.org/Water-heater-leaking.html

First thing is to protect your property from catastrophic tank failure where tank ruptures and water runs until it is shut off:
Tanks are under pressure when they are hot.
Close cold water shut-off located above tank.
Turn control knob to 'pilot' so pilot is lit but burner will not turn on.
Open hot side on tub for few moments to relieve tank pressure.

Now your property is safe.
You need a new water heater.
In mean time, gas water heater makes 41 gallons hot water per hour.
Shower used 5-9 gallons hot water.
Bath uses 10-15 gallons hot water.
You can turn on water heater for short stretches and limp by until you get a new heater.

Steps for installing gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

The first thing I would do is turn up temp control on gas valve.Control is located on front of gas valve at the bottom front of heater.They usually have a indicator dial on front with an arrow pointing direction.Turn dial to higher setting when burner is not on and this should turn burner on and provide hotter water. The control is normally turned clockwise to increase temperature.If control is already turned all the way up then water heater may need to be replaced.Depending on water quality in your area heater may have a large amount of mineral build up and it may not be capable of producing enough or hot enough water. If this the case all I can suggest is to try to drain tank and flush some of the deposits out. If you have installation manual it will give you instructions on how to do this. If not see if you have working shut off valve on cold water line ,if it works shut it off and connect drain hose to drain valve on bottom right side of gas valve. Put hose to floor drain or sump basin if you have one. Turn control knob on top of gas valve from on to pilot,this will leave pilot light on but prevent burner from working while draining. Open drain valve ,flow rate may be slow or not at all. Open hot water side of some faucet to provide air to help draining. You may try opening water supply valve to heater a few times to aid in draining. If you can get it to drain,shut drain valve off when done,turn cold water supply back on and shut off hot water outlet. Then when tank is full open hot water vavle to bleed air out of heater and piping. Turn control knob on top of gas valve back to on position. This should bring burner back on .It will take about 1/2 hour to heat. If you can't get it to drain or this doesn't help you might consider getting a new 40 gallon heater. Hope this helps. Thanks

your unit is undersized or you do not have enough gas supply to run the unit properly.
If you have to many water features running or you have to many gas items turn on at the same time it can cause problems.

On the back of the gas valve (where you turn the temp up) there is a stem that actually goes into the tank that senses the temprature of the water it could be dirty or buried in sediment depending on how old the tank is, or just bad. if the tank is over 10 years old i wouldn't bother replacing the gas valve, the tank is probably not far behind. A new valve will run around $100.00 maybe a little less. You wont find it at menards or home depot in stock but they may be able to order it for you. Menards sells rheem products or try you local plumbing supply house. REMEMBER TO RELIEVE THE PRESSURE ON THE TANK BEFORE YOU WORK ON IT. IF YOU CHANGE THE VALVE DRAIN IT FIRST!