Air conditioning fan stopped

The motor goes out quite regularly

Disconnect the cigar lighter and see if the short goes away, I will bet it does.

If your check engine light is on you usually have a code. Where I live several auto part stores will read the code for free. It would help to have a code.
If you have 2 fans on the radiator one should come on when you turn the A/C on. The other fan come on when engine reaches engine operating temperature. You have relay for compressor and the fan motor. Does the inside fan stop blowing. If a fuse was blown they should not work at all but a relay could drop out and in. I have found a bad relay over the years by checking the temperature of the relays, it is not always the case.. I have had a couple relays which were a lot hotter than the others, helped identify the bad relay. you can get the relay checked at the auto parts store. The low pressure switch could be creating problems with low Freon pressure. some info fuse relay below.
http://www.autogenius.info/chevrolet-cobalt-2005-2010-fuse-box-diagram/

So what does the fuse that blows, protect?

You need a wiring diagram & start to test
the components most likely to cause a high
current draw & blown fuse.

Don't keep replacing it.

You know the fan control circuit works, but the
compressor doesn't stay on. Did you monitor
the compressor as the fuse blew?

May have a module for compressor & fan
If so one side failed
The compressor clutch could be bad

Sounds like a blower motor... Does it work with the heat on?

If the blower is actually not operating i.e. you don't hear the fan motor at all, it is likely a blown fuse. When you stop if the air gets warm, it could be an indication that the system is getting low on freon.

Fan motor is not working.

may be a fuse, switch or blower. I would check all my fuses inside as well as under my hood, if they are all good, then I would check my switch, label all wires before disassembling, if switch checks out good then it will have to be the motor blower itself. Hope this helps Tim

Three possibilities;
All related to blown fuses,

1- Fuse blown in the engine compartment LH.
2- Fuse blown in the cabin forward LH below the dashboard (below your legs left hand).
3- Fuse blown in the harness (wire bundles) below the dashboard very easy to reach with your hands “just look underneath steering wheel ".

U said " The air conditioner blows, but the air is not cold.
" Yes only the fan working which might receiving power independent all from those other mentioned things.
If all fuses OK. Then look for broken wires.

Regards;
MAR

Make sure your are using the right amp fuse, if so you will need have the fan relay checked by a mechanic. The porblem would be in the wiring of the car since there is not much to a air conditioning system in a civic. As for the air not being cold you may have a leak in the plumbing of the air system that needs to be fixed because freon is very expinsive.