Supposedly, Apple does not warranty the earpod accessory that comes with the ipod. Although it is most likely that the earpods or the connector is at fault, there is a possibility that the pod itself could be mal-functioning.
My advice to you is to take the ipod and earpods to an Apple store if at all possible. You're more likely to get better service by presenting yourself in person, rather than talking to a rep over the phone. Plus, they can confirm that the problem is with your earpods, and if worse comes to worse, you can always buy a replacement if they're not nice enough to give you a replacement.