I am guessing it is not "shorting", but it is a cold/bad solder joint on the jack.
I have resoldered several headphone jacks in my day.
is it possible to open the beast and look for a cracked solder joint and resoldering it ?
typically this is caused by the stress of having headphones plugged in the jack, and movement the person wearing the headphones. so if the jack has been used a lot, that increases the possibility I am correct
Another thing that could cause the fatigue is if it is tight where the jack goes through the case of the player, and the player has been dropped.
another test would be if the problem still presents itself while using the headphones and wiggling the jack