If the problem is in the wiring (either at the plug or where the wire enters the headphone) a technician may be able to replace the plug or repair the wire. Not sure if the cost would be more than the price of the headphones.
I would suggest you contact Sony in your country. Sometimes they will take care of the problem out of warranty as a form of good advertising. Don't email them make a phone call. It's easier to say no in an email.