Faulty 3V solenoids

OK.
You seem to be talking about the "thermopyle" powered solenolds.
"Consumers" really should not mess with these. If the thermopyle doesn't put out enough juice to operate them, the solutions are: 1) ensure the pilot light is properly adjusted; 2) replace the thermopyle (they are relatively cheap); or call in a technician to service the gas valve assembly.
If you W/H doesn't have a pilot light most comsumers should just call in a tech. Many of these non-pilot light appliances operate directly on 120 volts and include a "flame detector."
They typically last DECADES without any attention although I had an "infant mortality" situation with a clothes dryer.
** Posted from **

I haven't seen a single one of these where the solenoid is expected to pull back the plunger. They have all used the manual "push and hold" button to move the plunger into place - all the solenoid has to do is to hold the plunger in that position, whilst the flame is present. Once the flame goes out, so does the plunger.
The electrical power generated by a pyro-electric flame sensor is pretty low, I wouldn't think it would ever be enough to actually retract a solenoid plunger.
I did come across one where the only fault was that the control valve assembly had moved back a fraction of an inch. So the push button was "bottoming out" on the carcase without having moved the plunger fully home. So nothing more was required than move the assembly back to where it had been. This had defeated the "engineer" called in to fix it, who, having replaced the flame detector with no improvement, had declared that a whole new water heater was needed as the control valve unit was no longer available but needed replacing..
-- Sue

There is no pilot light. There is no push button. When water flows a switch is opened and this fires the solenoid to allow gas to flow. It is not a thermopyle whatever that is it's just a simple 3V solenoid. The solenoid does pull back the plunger.

There you go, you see. A bit more information helps to replace the assumptions that will otherwise fill the void.
So, to return to your original question. You apparently have one winding with a DC resistance of 5.2 ohms and another winding with a resistance of 320 ohms. Your test meter almost certainly measures DC resistance.
You don't mention whether the solenoid is coupled to the gas valve when you carry out your test. If so, it could be the valve that is too stiff to move. With a couple of watt solenoid, there isn't a great deal of force available.
The sense wire is used by the controller to check whether the plunger is in or out. It won't affect the basic operation. I would forget about it, for the time being at least.
You don't mention how long it took the previous 5 to fail. Did they work for a while and then fail? Or did they fail, right out of the box?
Solenoids are extremely reliable as a rule - which is why they are used as interlocks in many safety-critical situations. One cause of failure can be over-enthusiastic or inappropriate lubrication of the plunger. Another can be mounting at an angle not designed for. eg most of the problems are from misuse, rather than being inherent.
So, lacking further information, I assume that the solenoid is actually coupled to the gas valve when you carry out these tests and that the fault lies in the gas valve, rather than the solenoid. However, more facts may discount this hypothesis.
-- Sue

[snip] If there is no thermopile, then what is the power source that is used to pull in this solenoid?

Presumably the electronic controller. Although 3v, or thereabouts, does seem an unnecessary low voltage to use.
-- Sue

It is powered by a 3.3V regulator. Originally it was powered by 2 x 1.5V batteries. It is definitely the solenoids that have failed there is no gas valve. The plunger retracts and gas flows through the gap. My original post explains how they fail. They work for a few years then fail.

Was this system originally designed to operate with a fixed 3.3V regulator? Or 2 batteries? Either of these seem like a pretty unusual system. Nothing like what I've ever seen.
Here's my guess: The coils were originally intended to operate off of a thermopile. While its open circuit voltage may be a couple of volts, under the load of the solenoid, that will be reduced, as will the current. Somewhere along the line, someone made a re-design (or a hack) and ran the same coil off of batteries. The coil, not being designed to run off of such a source, is now suffering from reduced life.

Several things spring to mind. The first is that this solenoid, from your figures, would have been taking about a half an ampere hour from the batteries. For a system where the solenoid could be needed to be engaged for many hours a day - this was hardly likely to be a successful design.
Next, from your latest description, this isn't just a solenoid - it is an electrically operated gas valve. There must be gas-tight seals involved somewhere. If these seals are around the plunger, it may be increased stiction with these seals that is causing the problem. This is easily proven - use a force gauge to measure the force needed with an (unenergised) new valve, compared to one that has "failed". If the force is greater with the old valve, the problem isn't electrical, it's mechanical.
If that is the case, then "a few years" may be the design life for these valves, when used with gas. Gas does tend to be much harder on seals than, say, light oil. These valves may have been primarily designed for the latter, although also rated for gas.
If the force gauge reads the same with old and new, then there is one other possibility - permanent magnetism. It could be possible, for a number of factors, for part of the magnetic loop to have become permanently magnetised, in opposition to the energising magnetic field. This can be proven by reversing the power supply connections, but don't do this with the sense wire connected! The solution to this is easy - "degauss" the solenoid. This is normally done by placing the object in a strong AC magnetic field and slowly reducing that field to zero (typically by slowly removing the object from the field).
-- Sue

No the califonts originally took 2 X 1.5V batteries. I removed them and hooked up 3.3V regulators instead. This has worked well for a long time. Could the fixed 3.3V cause a problem as opposed to batteries? The voltage under load is 1.57V using the fixed 3.3V input. All the voltage and resistance measurements I have given are the same on faulty and working solenoids.

All there is is a solenoid plunger with a spring and small round rubber seal on the end which covers the gas inlet hole. The problem is with the solenoiid alone - I tested them all in isolation, removed from the system. The plunger moves freely in all cases.
I have tried reversing the inputs and it just does the same thing, i.e needs help to retract and then pops out when the power is turned off. What am I looking for if I reverse the connections and there is permanent magnetism?

I have exposed part of the core and put a small screw near it. I feel no pull or push. I also tested one solenoid with the spring removed and it worked suggesting that the magnetic field has weakened or has an opposing permanent field. Where do I find a strong AC field and how do I reduce it to zero?

I have combined your two posts to answer them together.
If reversing the input doesn't produce a change then it isn't a permanent magnetism problem. The permanent magnetic field that hindered with one connection would actually assist with the reverse connection.
However, for academic interest:
As to the strong AC field- your local scrap dealer may have a one hanging from a crane. Good blacksmiths have one. You can buy "demagnetisers". Or, it is possible to make one.
To reduce the field to zero, you either connect it to a variac and turn that down or, even easier, slowly move the item further and further from the demagnetiser.
But back to your problem - what you need is a working one and a non-working one side by side. Swap the springs. If that transfers the problem, then you know that it is the spring. As you have discounted permanent magnetism effects, a change in spring properties is the next most likely..
-- Sue

Ok this is rather embarrassing. But not my fault! Our maintenance guy had written dud on all the solenoids but he tested them outside the califonts. Turns out they need to be in place with the spring already partially retracted to work. Also he tested one or two in place but the machine may have had a faulty control board and the sensor wire may not have been working. Thanks to all who replied and sorry for the waste of your time.