Suburban Water Heater gas will not shut off

There are NO Individual Shut-Off so with propane valved in you will have propane up to AND thru the water heater Gas Valve

You have TWO Issues:
TURN OFF PROPANE
1) In order to have the small flame where you have indicated with the Yellow Circle you have to have some 'Blow Back' as that area is the air venturi opening......ignition source is all the way at other end of burner tube.
So for Flame to be there in venturi area the Main Flame had to come back up the burner tube....THAT is due to dirty Combustion Chamber/Burner Tube
You should remove burner tube///clean it out, clean the Combustion Chamber (run a wire thru it and out exhaust/tie rag to the wire and pull it back thru (have to remove exhaust shield)
Clean orifice by soaking in alcohol Air Dry (No High Pressure air or Poking anything thru it)
Reassemble and TURN Propane Back ON

2) Gas Valve IS leaking thru....springs inside the solenoids CLOSE the valve
Both Solenoids have to be working in order to OPEN valve
Could just be some debris in the Gas Valve not allowing it to fully close.
Cycle the Gas Valve couple of times......Fire it Off---let Main Flame burn for a minute or so then turn switch off. Repeat and tap solenoids each time

Check with sniffer if gas is still leaking thru
NO.....might be OK (probably show replace anyway)
YES......TURN OFF PROPANE and LEAVE OFF until New Gas Valve is installed

enblethen wrote:
Driving down the road could blow out the small flame setting you up for a larger issue. Boom!

Yes, make sure to turn off propane tanks when traveling to your destination.

Driving down the road could blow out the small flame setting you up for a larger issue. Boom!

One thing you could try for now is fire up the heater and get the little flame happening. Turn off the heater and tap the solenoid a couple times, see if the flame goes out. If it does, do this after each heater usage until you replace the solenoid.
If it doesn't, make a shield out of tinfoil just above the burner tube to deflect the heat. I don't think the heat would bother the wires or solenoid, but a shield would give you piece of mind.

Cycle the water heater a few times. Presume by your post you just bought it and who knows how long since it was run.
May get it working right again.

Replace the solenoid valve assembly!

Here is a photo of it. I also noticed the solenoid housings are plastic, so I’m not sure if that’s an issue with the flame nearby either.

Try to move the wires away, or wrap a bit of tin foil around them. The only problem with turning off the tanks is, no stove, no furnace.

Post a photo, use this link to post a photo.
http://photoposting.is-great.net/?i=2

Thanks Boon Docker. I was concerned about leaving the flame there with the electrical wires nearby, as the flame seemed to be fairly close to them while it was dancing around. Do you think it’s safe to leave there or will we need to open and close the gas bottles?

Thanks,
Brooks

Does seem like a faulty gas solenoid valve. Do not blow out the little flame. You do not want a build up of propane that can explode when the water heater fires up.
I don't think you will be able to turn off propane without turning off the propane bottles.