Ceiling fan low speed (only) once on slows to a stop
I can think of a number issues that may be affecting the low speed. 


Is your mains voltage a little low? A low voltage could keep the motor from generating enough torque to overcome the bearing friction. 
Is this an old fan that has seen a lot of usage? It could be that the bearings are worn or need lubrication.
Is the fan fully balanced? Even a little imbalance could be causing an friction variation on each rotation in the bearings that is not overcome by momentum at low speed.
Is the fan hung in a way that it is not vertical (with the fan being off the  horizontal)? Seems like this could possibly impact things similar to item 3.
Is there dust, dirt, cob webs or other crud down inside the motor in the narrow gap between armature and stator that is adding extra friction making it harder than necessary to turn the motor?