You will begin to shift from a fixed to a variable reinforcement schedule. A fixed schedule means that a standard unit of behavior gets a reward. Touch the cone, get a treat. The horse knows exactly how much effort he needs to put out to earn his treat. Fixed schedules create limited results.
Variable schedules create excellence.
If your horse stops strongly touching the cone, move it back to a height where it is easy for him. Reestablish the behavior and then go on to increase the difficulty. In a variable reinforcement schedule the reward is unpredictable. Since the horse never knows exactly when his treat will come, he keeps offering more behavior. Touching the cone got a click last time, but now it's not working, so the horse tries bumping the cone harder.