After start up the fryer could work for a while until it reaches temp and then it totally shuts down burners and pilot. If try to relight pilot most of the time will not relight or stay on. what is the cause of this.

SOURCE: problems with fryer

your problem is the thermostat is bad.the reason it shuts down is that it trips the hi limit.the hi limit is a saftey device that shuts the system down so the oil doesnt get too hot and catch on fire.remove all the oil from the tank and you should see 2 skinny metal bulbs one is the hi limit bulb the other is the t-stat bulb,make sure they are secured to the bracket.if the t-stat bulb isnt you will also have this issue,simply reattach it.let me know.

SOURCE: ifs40 w/ new thermopile

If the pilot shuts off within seconds of the burner, I strongly suspect you are having a problem with the hi-limit circuit. Check your wiring. The slightest unwanted grounding will cause the valve to drop out.

You also need to inspect the mounting of the bulb for the high limit. Make sure it isn't covered in debris. It should be clamped close, but not touching the heat exchanger. Grease needs to be able to flow on both sides of the bulb.

You'll need to test the switch with a meter or a jumper (for TESTING ONLY!). Remember, the hi-limit switch may be doing it's job and be the symptom, not the cause. But if the switch is tripping open prematurely, you'll need to replace it. (Part# 1177) Are you testing with enough oil in the vat?

SOURCE: Imperial fryer IFS-40

I had a very simular problem. My fryer would do exactly as you described, but sometimes the pilot light would stay on until the burners tried to re-ignite and then it would go out.
I finally had to call the gas company. They took the pilot light apart and cleaned it. The fryer works perfect now.
Hope this helps!
Ken