@dpesser , David, could be a faulty charge port, first check for dust debri and blow it out, also look inside to see if contacts are bent and straighten with a pin if bent. Could also be a faulty battery if older consider replacing it.Links below for trouble shooting and replacing charge port and a link to charge port and battery for 3DS. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
https://www.youtube.com/watch?v=oZrprlK7PbE
https://www.youtube.com/watch?v=0_8XEsi-0G4
https://www.amazon.com/Socket-Connector-Charger-Charging-Nintendo-Replacement/dp/B0098GIQYY