I don't think many people here, myself included, have any experience with your problem and that is why you haven't received any suggestions.
A couple of random guesses that might help with troubleshooting:
- The long extension cable could possibly change the impedance seen by the headphone output and it just isn't capable of driving it properly. Have you tried not using the extension cable to see if the problem occurs only when you use the extension?
- The connection between the extension and the headphone's plug is not secure. Is it a standard 1/4" plug on the headphone cable or is it a 1/8" mini plug and you are using an adapter? If you are using an adapter, is the adapter a stereo plug (tip-ring-sleeve; 2 colored bands) or a mono plug?
- Is the cable near an antenna? The long cable can act as an antenna itself and that could cause interference.