Insulating funnels, called electron hop funnels, use secondary electron emission and an electric field created by an electrode to transport current through the device. The surface charge along the funnel wall self-adjusts to get unity-gain transmission. Electron hop funnels allow increased control over the spatial and energy uniformity of the transmitted beam from a field emitter array. Measurements performed on the relationship between transmission through the device and the electrode voltage has shown hysteresis. To better understand the origin of the hysteresis, simulations have been performed using the particle trajectory code Lorentz 2E. The simulations reveal two very important mechanisms that define the transmission through the funnel. The simulations also show that hysteresis is a fundamental characteristic of hop funnels.