I'm assuming that this "backphone" is just a set of wired headphones but with the plastic around the back instead of over your head. If that is the case I have the following suggestion.
buy a soldering iron and pop open the headphones. Find the wire that when you shake it, the sound cuts out. Check the connection, and if it looks lose, then re-solder it. Else, you could just replace the entire wire. It'll save you lots of $$$ over time if you do this for all sorts of electronics and you'll even learn something along the way and it really isn't all that hard.
Your headphones may not look as pretty, but it would cost you ~$0.50 if you already owned a soldering iron and solder. If you had to buy a new 1/8" plug, then that would cost you ~$3








