The timer is Low speed only, then you change to High speed with the relay, right? So the tripping is happening twice per day when the timer turns it on for Low speed only; switching it manually to High does not cause a trip. Right?
My theory is that after it has been OFF and cools down for a while, condensation is forming in the motor peckerhead, then when the timer tells it to turn on, the power tracks to ground briefly and the GFCI trips. But after it trips and is reset and started again, there was enough heat that the moisture evaporates and everything works fine again, until the next time the motor is off for a period of time. It also works fine when you are manually switching to High speed because at that point, it was ALREADY running at Low speed and warm. The test might be to wait until it trips again, then have them leave it off until you get there. Open the peckerhead and spray some WD-40 in there, see if that helps. Or put a space heater in there to keep the motor warm. If the timed function no longer causes a trip, that was it. Then you have to figure out why moisture is condensing in the peckerhead. If there is a conduit going into the motor that is open to the air, that may be why.