You did try the headphones on more than one source to make sure that it's the problem?
The problem might be a broken wire in the cable. This often happens where the wire enters the 3.5mm plug. On most headphones the plug can be replaced but it requires soldering skills.
If the problem is in the left side ear piece you would have to open it to check the speaker inside. It may not be possible to get a replacement speaker to fix the problem.
Given the going price of the headphones I suspect having to pay someone to check the plug and replace it will exceed their cost.
I had the same problem, it comes from the little case were there is the microphone and the pause button, "all" you have to do is open it (using a knife or something pointy), take out the cables and try to isolate the cables that are going farther up and the card (I used some tape) and close it again (I taped it on the outside to be sure it doesn't open). I wouldn't do it if you still have a guarantee or something like that but otherwise it worked for me. Good luck