I HAVE A FIX!!! This happened to me and I couldn't figure out why. I contacted Thrustmaster and had EVERYTHING checked. They found no issues. HERE'S THE FIX:
Recalibrate your pedals in GT7. BUT! Do each pedal separately and REALLY, REALLY SLOWLY. Like, as slow as you can possibly manage. It seems to register inputs bit by bit, so if you calibrated by stamping down the pedal, it reads 0% + 100% and nothing else. If you do it too fast it records (for example) 0%, 25%, 70%, 100%. Anywhere in between those recorded inputs is basically ignored. So 25-69% would result in 25% input, then 70-99% as 70%. 100% becomes one, flaky input; one number in 65,536 possible inputs – the accuracy of the pedal set. Drop off that specific input, and you lose connection until you reapply the pedal. I hope this helps others out there. Let me know.