Jump th terminals - Hayward 250kbtu Ng Pool Heater - Inground

The fact that it starts when you jump it makes me believe it is not the started. I think a dirty, loose, or bad battery cable connection -- or it could be a bad battery cable itself.

You said you jumped the wires for the pump? Was that at the pump relay?
If you have a voltmeter or test light, keep the jumper wire in place and check for voltage at the fuel tank connector. The pump wire will be gray. With relay out and jumpered there, you should have battery voltage at the fuel tank connector. The key doesn't even have to be on, cause the relay has voltage to it at all times. If you jumpered it right (terminals 87 and 30 on the relay), and no voltage at the tank connector, you have a broken fuel wire somewhere between the relay and the fuel tank.
If you do have voltage at the tank, but the pump still won't work, only two possibilities, a bad pump or the ground for the pump is lost. Check the pump ground first.

check how many millivolts the pilot is generating. if pilot stay lit and burners wont fire u have a problem with one of the safties, lose wire connection, tstat control

I have an H300 Millivolt Hayward heater. It will start and run for about 1 minute then shuts off along with the pilot going out. I've tried cleaning all the terminals and running all new wiring but same result. I've also jumped out the TH to TH terminals leaving the jumper in place and it still shuts down after 1 minute. Any idea what that could be ?

on gas valve, jump out th and tp terminals. if still no flame, replace gas valve

pull the 2 wires off of stat and twist together if unit come on its the stat if not go to the gas valve and jump out to see if the valve will come, the 2 th terminals.

If the (th) terminals means the thermostat terminals then you have a bad thermostat and it needs to be replaced.

I have the same heater and have been struggling with it since we purchased our house 6 years ago. I am very familiar with the "tapping" method and just this year learned that I could jump the TH connections to consistently get it to light. Finally that too became unreliable as the heater would shut off shortly after I jumped it. I used a voltmeter to test the millivoltage coming from the pilot generator (assembly) and found that it was only around 300mv, whereas supposedly 500mv is required to open the gas valve. Before investing $70-$100 on a replacement pilot assembly I decided to take it apart and see if it needed cleaning. There was a bit of buildup on the thermocouple that I removed with 150 grit sandpaper. I re-installed the pilot assembly, lit it, and retested the mv. I was disappointed to see that the millivoltage was still only around 300, but as I watched it began to rise until it eventually reached 500. I then turned the thermostat on and adjusted it until it was higher than the temp of water and the heater instantly turned on. So far so good....

are you sure your jumping th and th/pp? the labeling on valve is a little deceptive.should use 1st and 3rd terminal on gas valve. if your using correct terminals try same thing with thermostat wires disconnected from gas valve. this will isolate valve from all controls and safties.if it fires valve is good and need to look in thermostat loop for problems. hope this helps