The left earbud has stopped making sound. - Skull Candy LINK Earbuds Consumer Headphones

SOURCE: Sound in left earbud shorts in and out

If its not hard to open the case, just solder the connection again (only if you found out that the problem is inside).
Also check the wire if it have 100% connection. You may also check skin of the wire. If found out no good, so possibly this could fix the problem.

SOURCE: Sony MDR-NC11 Left Earbud has no sound

They should come apart right where the metal meets the plastic, just below the buds themselves - be careful, one set like that I took apart were actually surface-mounted to the housing, there weren't any leads to repair...

SOURCE: Left Earbud Went out randomly

The only thing you can do is to replace it.

SOURCE: left earbud problems

Well, I had the same problem with the right earbud. Luckily I was under warranty with Target, so they told me to contact Bose. I did and they had me send in the headphones (to make sure I waas telling the truth) and about 2 weeks later I got my earbuds back. Their customer service is excellent, so that's what I would reccomend