Try playing your headphones at very high volume (louder than you would want to play them if they were on your head) for a few hours.
I've found that my older Stax headphones sound similar to what you are describing if they are not used frequently and/or given that kind of workout from time to time. That has been the case ever since they were new.
The fact that the symptom is not exhibited by different Stax models which are copper cabled does not by any means necessarily indicate that the cable material is responsible for the difference.
Regards,
-- Al