Preface: Don't do this, just go through the support team and have them fix it.
So my Pod Go was having the same problem. Not an intermittent connection, no connection at all. Tried a couple different computers, 4 different usb ports (which all worked with other devices) and after reading this thread, I determined that it must be a hardware issue.
Grabbed a screwdriver and a 11mm socket and took out almost all the screws off the back plate and set it aside. The top board is the one with the USB connector on it but it's held in with the 8 input and output jacks on the back of the unit.
It doesn't look like there's really any way the USB connector could have a bad solder. All of the solders points are on the face-up part of the board and are clearly visible without removing it. There are two grounding solders on either side of the connector on the upside down side. More importantly, there is a connector between the two circuit boards which is only accessible by getting the top board loose and flipping her over.
Take out all 8 of the silver connectors. Don't lose any of the black plastic 'washers'; they are on both sides of the housing. The big ole wide ribbon cable connects the top board to the bottom board which is what makes the display work, don't mess with that.
I initially thought that this connector with 4 wires could be something to do with the power to the display but it is labeled 'USB' and it does line up with the physical USB connector. Turns out one of the two connections was loose. For mine, it was the side connecting to the top board. I unplugged it and it came out of the socket really easy (not a good sign), and put it back on. There was a TACTILE clunk when it put it back it. It makes me think that it wasn't properly put in at the factory. There are bits of hot glue on either side of the connector, but that doesn't do much if it's not plugged in all the way in the first place.
I tested it before re-assembling it all the way and it connected to my PC perfectly and I even installed 1.3 before putting the back plate back on.
Pretty annoying but I'm happy it works now.
Obviously I don't work for Line6 and I'm sure this potentially can void a warranty or something. I was super careful and intended to stop fiddling with it before doing anything destructive. In retrospect, I would've just gone with the support team and had them fix it for me.