Ok, this is the second radio this has happened to me with, I couldnt find a repair article on it. If there is one, disregard this. If not, great! I am unsure of the model number on the radio but you can look at the pictures to see if its yours! Also I cannot confirm it but the problem is probably very similar on the other head units in the mopar family with similar AUX connections. So lets get started.
The tools I used:
Philips Head Screw-driver
Small Flat Head Screw-driver
T10 Torx Screwdriver
Step 1: Remove Radio Head Unit
Already dropping the ball, I did not include this step in the write up, but here's a link on how to do that because someone has already written one.
How to remove the radio *
Remove 4 Torx Screws on face of head unit
I used the T10 Torx size, it seemed a bit small but it worked and the next size up didnt fit (T15)
Disconnect Wires from the Head Unit to the Head Unit Face Plate
Carefully pry up on the white connector from its sides with the small flat head screw driver
Remove Volume and Tuning Knobs
Just pull on them and they'll pop off
Flip the Head Unit Over and Remove 7 More Torx Screws
Remove Head Unit Face plate
WARNING The AUX reciever (Small silver ring) is loose and may fall out during this step, be vigilant!
The face plate should just slip off
Remove Rubber Pad and Locate AUX Connection
Remove "Busted Lid" off the top of the AUX Connection and set aside.
Heres where we can start to see the damage, I believe this is the main issue of the "loose-ness"
Remove AUX Receiver (Small Silver Ring) and Solder
You should now be able to view the square-circle metal plate and it will probably have a gap in it like the one pictured. You'll need to solder a bridge in the gap, after that you can add some solder to the face of the plate so you can solder the AUX Reciever to the plate
Replace AUX Receiver and Solder
Grab the AUX Receiver with the pliers and hold it in place while you heat it up with the soldering iron, this should melt the Soldering metal underneath it, connecting the AUX Receiver to the square-circle plate
Glue "Busted Lid" Back on
I dont know another way to do this, I used Epoxy, but super glue should work just as well, if anyone could improve this step, please chime in. Like I said, this seems to be the main brunt of the issue. (Sorry for the bad pic)
Let the glue dry!
As the Haynes Manual would say, "Installation is reverse of removal"
If you did it right, everything should work fine and dandy! Until it breaks again...