http://www.walmart.com/ip/Sol-Republic- ... l/48714064
For the longest time, we didn't know how to open the speaker so that I could re-solder the loose wire, and I did some endless searches on the internet but couldn't find an answer. Then, as I was messing with them, I was able to pop one of them open so I could see how they were assembled. So if you need to know how to repair these headphones, the info is here.
The ear cushion side of the speaker swivels against the base side (the side that attaches to the headband). As you can see in the pics below, there is a male plastic clip on the base side that fits into a female clip on the speaker side, so to open the headphone, you just need to slide something (preferably a plastic putty knife) into the gap between the two sides and pry them apart.
There are two small wires that come out of the speaker side and are soldered to the connector on the base side. In pic #7 below, you can see that, even though the wire is still attached, it isn't properly connected. When I re-soldered the wire, the headphone started working again.
You don't need to disassemble the base side, but I disassembled it anyway so I could take some pics and those are the first few pics below.

