Q: Why do the buttons on my earbuds not work?

There are a few things you can try.  The first is to simply reset the Shuffle as it may be the cause of the issue.

Resetting iPod shuffle

Otherwise, also make sure that the earbuds are plugged all the way in and that the white part of the headset is flush with the body of the Shuffle.

If possible, use another set of earbuds to see if they work okay. If they do, we know its the headset that is the problem and from there you'll need to take the necessary steps to replace them.

B-rock

It might not hurt to do a full restore of the Shuffle in iTunes as well to make sure that the issue isn't the result of a software error/glitch or corrupted data. 

Restoring iPod shuffle to factory settings

Sounds good. Let us know if the new earbuds take care of the problem!

B-rock

There is a replacement program in operation for these headphones as apple is aware of the intermittent problem.

There is however a two year limit on the replacement