Technically, a GFCI protection device (receptacle or circuit breaker) operates by monitoring the imbalanced current between the hot and neutral conductors. In a perfect 2-wire AC circuit, the current returning to the power source will equal the current leaving the power source. If the difference between the current leaving and returning through the GFCI sensor exceeds 0.005 amps, the circuitry opens a switch within one-fortieth of one second and de-energizes the circuit.
First thing to do is check if the GFCI itself may be bad. Push the test switches on the receptacle or breaker. If they aren't working correctly, replace the GFCI. They can stop working over time, especially if they've been reset a lot. If the GFCI is working, try plugging in a trouble light or other item and see if it holds. If all is OK at this point, then the heating element (and associated wiring) may have developed ground paths. Last thing I can think of is that something in the construction or operation of the heating elements may be fooling the GFCI. For example, I assume there is a thermostat or over temp switch built into the heater circuitry. This may cause enough of a variation that the GFCI sensor picks it up. Sometimes very slight current variations cause the GFCI to trip even though everything is functioning properly. Contact Luhr Jensen and see what they have to say.