Either something is stuck or it's damaged. The actual connector inside the port likes to separate into two pieces after a while. Then you jam in the charge cord and damage the connector. Really common. If you take a close look into the port you can usually check and see if there is any noticeable damage.
Hopefully its not broken, as it's a rough repair to replace the chargeport. I would take it to an awesome technician unless you want to break the LCD and be stuck with a $150+ repair!