The OP should be confused after some of these replies. A little dust should not. Make the connection loose. Take it to the Apple store and they will replace. It is a rare but known problem.
Actually, I just had this exact same issue, and it WAS just compacted dust and pocket lint in the back of the lightning port of my iPhone 5 that was making the connector loose (and I mean so loose that I could barely get it to charge). I used a soft toothpick and dug out more crap than one would think could be hiding in there, and now my lightning cable is totally snug again and charges flawlessly.