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.

How to increase gas pressure of pilot lite for imperial deep fryer?