The cigar lighter element may be bad, or the prongs may not be making contact. You could try bending the prongs out a little with a screw driver.
Also, you could try a replacement cigar lighter (knob & element) sold at Pep Boys, but I don't know what kind of quality they are. Try looking online for a replacement.
Edit:
I forgot to mention that you should disconnect the ground cable on the battery before tinkering with the prongs in the cigar lighter.
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