If you are saying you cannot get the oil hot enough during pre-heating:
- You may need a bigger burner than the one you are using. Most resources I've seen suggest over 100k BTU
- There may be something physically wrong with your setup (i.e., the vessel should be closer to the flame)
- The ambient temperature at the time of cooking was simply too cold for the burner to keep up (see problem 1).
If you are using a purpose-built commercial turkey fryer, I suggest consulting the book or contacting the company. If you built the rig yourself, I suggest more fire! (and lots of safety precautions)
Now... if you are talking about a temperature drop after you dunk the bird, realize that is totally normal.
Alton Brown suggests a preheat temperature of 250 degrees. He suggests raising the temp to 350 after the bird is in the bath but adds the following advice:
"Closely monitor the oil temperature: it's will start to climb above 350 as moisture cooks out of the turkey; reduce the gas flow accordingly..." (Ref ep. 163 transcript in his book Good Eats 2, page 413)
You may need to use a smaller turkey to achieve the internal temperature you want without burning the outside. I'd look for something in the ballpark of 10 pounds. If you are cooking for a crowd, it's best to go with multiple birds instead of going bigger.
Be mindful of carry-over cooking:
Even after it’s been removed from a heat source, food continues to cook. Its internal temperature can rise anywhere from 5 to 20 degrees. The larger the food, the more carryover or residual cooking you’ll have.