I have a ceiling fan that works fine on the medium and high speed settings but does not work or rotate on the low speed setting. What is the cause and can I repair it?

3 speed fans have 2 windings. Low, medium, and high use one, the other, and both. As long as high speed is still faster than medium, that means the low speed winding still works, it just isn't switching correctly. Check the connections at the switch. If it is a manual switch, the hardware store should have a replacement. If it a remote control, it may be harder. It could be the remote or the switch at the fan. Perhaps where you bought the fan could help.