Take a second to look at the back of your Go-Pro. Look at the slot that the charger typically goes into. Does it appear to be aligned with the casing? If not, this could be the first problem. In order to fix this you must pop off the back of your go-pro. Take into account that your Go-Pro does not actually come out of the clear skeleton case. Instead, the grey or black chasing should come off with a little leverage.
If you're having issues doing this, look up the device page on Ifixit and the guide for this will be there.
If everything looks aligned, and there are no crumbs or small bits clogging it, then look at the charger itself. Ensure that the end of the cable doesn't have anything stuck in it (i.e. food, dust). If it does, take tweezers and attempt to remove the small pieces.