What would cause a pet scan to not detect malignant melanoma that was about the size of a chocolate easter egg? I also have type II diabetes.

Many Factors. No test is always right, pet/ct included. Every patient's tumor is unique, too. How a particular tumor will take up the primary pet/ct tracer, called f-18 fdg, is also not perfectly known. Some consistently fail to take up FDG that pet/ct is rarely used to image them, but this is not true for melanoma. Finally, smaller tumors are always harder to see, no matter which imaging technique is used.
Information. Pet scan is not an absolute diagnostic tool. It depends on how it is done and by whom. False negatives are a definite problem with the test.