GFI's (Ground Fault Interrupters) are designed to protect users from electrical shock by interrupting the power to the outlet when there is a difference (leakage) in the currents in the hot and neutral lines.

The UL requirement for GFI is that it trips when there is 5 mA of leakage current while the regular 15 amps circuit breaker will do it only if it's 15 amps.

Leakage in electric motor windings to ground is very common and as long as it is less than 5 mA, GFI does not sense it. With age and dirt it leaks more and more, and finally it's getting over the GFI limit while it is still safe with properly grounded regular outlet and dryer.

I would plug the dryer (using a three prong power cord) in a regular grounded outlet with 15 or 20 Ampere circuit breaker.

Here are the break down diagrams for the Whirlpool dryer Model LGN2000KQ0

Gene.