Well...actually what I meant by a bad ESC is maybe it's defective? How long will the motor run at half throttle?

It does sound like the battery is being pulled down below the LVC (Low Voltage Cut-off ) at high throttle settings, but the servos should still work, especially if the ESC is not overheating.

Which ElectraFly battery do you have? A 3 cell but of what capacity?