Make sure the propeller spins easily on the shaft, a likely scenario is that in your programming the pump is restarting at a low speed, it doesn't have the umph to get going because the prop/magnet is slightly stuck to the shaft by sand, debris or calcium build up. The shaft stays still and the magnet with prop spins on the shaft. Unplugging it works because your program likely pulses up to 100% or a higher speed and that gets it started and then it can keep going once the initial start up resistance is overcome.
Also, be sure you only have made one adjustment, i.e. if you have a controller the potentiometers on the pumps junction block where the power and controller connect, must be at 100%, this adjustment is never used if you have a controller.