iPod won't take charge. How can I get lightning connector fixed?

I have a 5th generation iPod touch that I got in 2012. In the past couple days I notice the charger I just bought wasn't staying connected unless I held it a certain way. So I figured it was the charger I bought. So I used the old white one I've had. It seemed to work fine. Then I notice I'd have the iPod on the charger for a whole hour (it shows bolt to say its plugged in), then I unplug to go somewhere, and it immediately says low battery. So after trying multiple charger, usb adapter, etc. combinations I have come to the conclusion that the pins inside the lightning connector of my iPod are too worn down to take a charge from any adapter.

Is there any way to get just the connector on the iPod fixed? or any way to create a solid enough connection so I can connect the iPod to my iTunes and do a full back-up one last time?