Lie up deep fryer

Check the gas pressure, it must meet the standard gas pressure written on the nameplate. Check also the quality of pilot flame, poor pilot flame quality will not properly heat up the thermopile which in turn will result in poor fryer operation.

If the pilot flame does not hold after releasing the button for at least 20 to 30 seconds, try to clean the thermopile and tighten all wiring connection on gas valve, thermostat and hi limit the repeat the process. The thermopile must be heated by pilot flame in order for it to generate small amount of voltage to open the pilot valve.
If this does not correct the problem, try replacing the thermopile.

Try first to clean the thermopile. If it has accumulated soot/ carbon, it will not sense enough heat from the pilot flame to generate small amount of electricity to energize the pilot valve and main valve of gas valve.

Check if the unit receives the right amount of fuel as stated on its nameplate, if it does, check all wires for loose connections, Milli volt wont pass on loose wiring. If this does not correct the problem, you have to replace the gas valve, the main valve coil may be shorted that's why the pilot is shut when main valve is energized.

Check if the fryer receives sufficient gas pressure as specified on nameplate, if so, your pilot orifice may be clogged.You can clean this by removing 2pcs pilot screw (+) then dismantling the pilot assembly using a vise grip and an adjustable wrench. Once the pilot hood is removed, you will see the pilot orifice. Make sure that the hole will not get large when cleaning.

Have a lighter handy (I use one of the elongated ones for caravaners)
in-between the burners is a pilot light (top right) keep the lighter flame where the gas comes out.
On the right hand side of the fryer at the bottom is a gas valve with a little black knob.
Press and hold the black knob in and gas will come out of the pilot light and ignite by the lighter flame. You need to hold the button in for quite a while. (until it stays lit)
When it stays lit depress the little black knob and turn it anti clockwise. Gas comes out of the burners and ignites from the pilot light. When it reaches temp. it will cut out.
To turn it off turn the little black knob clockwise. To turn the pilot light off, push and turn clockwise.

Two things to check. Make sure you have continuity through the terminals on the high limit. Also make sure you have a good pilot flame and the pilot generator is supplying over 500 millivolts. It's either the high limit or the generator.
Tom

When you turned on the thermostat you required more millivolts from the system and it failed. Low millivolts. That would tell you the pilot generator needs replacing. Make sure you have a good pilot flame hitting the pilot generator.

Tom

Check if the flame quality of the pilot is good. Small amount of voltage generated by thermopile used in energizing pilot main valve coil during fryer operation relies on the quality of pilot flame, also, the thermopile itself should be free of soot or any form of dirt in order for it to absorb the heat from pilot flame.
Check also the gas pressure, it should meet the gas pressure required on the nameplate.

This problem could be caused by a few different things. You should check the condition of your pilot and the thermocouple, if the pilot is weak due to being dirty you will not generate the optimum Millivolts to run the fryer, you may need to dissassemble and clean the pilot. The thermocouple needs to be correctly placed in the pilot assembly, if it has dropped down to where it is not in the flame it will not work correctly. You may need a new thermopile as it may not be generating millivolts as needed. Gas pressure can cause this as well, if the pilot goes out then the main burners come on you should check the gas pressure. One more thing to check is the hi-limit thermostat, if this is cutting out early your pilot will go out. Imperial uses a self-resetting limit, after a few minutes your fryer will relight and work until if cuts out again. If your fryer pilot stay on with the thermostat off for long periods of time and does not go out immediately when the burners come on and the pilot is clean, you may need a hi limit. This is a lot of info, I hope it helps.