It is most likely a dodgy charger - or USB cable if the charger uses one. Basically, micro USBs are extraordinarly femer and damage easily. The charger that came with my last HTC literally lasted 4 charges before dying.
Try a different charger (friend or colleagues?) to see if that fixes the problem. If it does, you can get a new charger/USB cable from ebay for peanuts. Be sure to check that a new charger provides an adequate amount of juice. If you don't buy a 'genuine' charger, be sure to check the Amp rating on your current charger and the advertised rating on any new one.
If it's not the charger, then I'm afraid it's most likely the USB/charger port on the phone and you'll need to send the phone for repair.