Hi, I''m sorry you're having trouble with your pool heater.
The pilot in your heater generates the power to open the gas valve. This operates on a tiny d/c voltage signal of 750 milli volts. Way less than 1 volt. Since we are using such a small voltage, any kind of poor connection will interrupt the power to the valve.
You need to inspect each wire connection for loose or corroded connections. The next thing I would do is check power from the pilot generator and make sure you're getting enough voltage. A dirty pilot burner can cause a weak voltage output. I won't go into detail here, as there is a very good electrical trouble shooting guide in the download I'm attaching. They explain it better than I could. It will require a volt meter capable of reading millivolts to test.
The other prime suspects in these pool heaters would be a defective temperature limit switch that acts up or even the temp sensor that plugs into the board. Page 32 describes how to test the temp sensor.
Without a meter about all you can do is 'jumper' the temp switches one at a time to see if it will stay running. This may help isolate the defective component. This would be for diagnostic purposes only, and any jumper wire must not be left on.
I would start with a millivolt reading. Without that you really don't know where you are. If you do not have proper voltage from the pilot generator you'd be wasting time checking anything else.
Let me know if you have questions as you progress. I'll be happy to help.