as you can see in step 11 of the [guide|427|shuffle logic board guide] - the jack is soldered to the board.
normally it's only "dirt" inside the jack or one of the contacts is bent. since the headphone jack is "open" - you could see one of those problems when the shuffle is opened.
another possible problem is a proken soldering point/contact between the headphone jack and the logic board. if you have a soldering iron (and are able to use it) - resolder the headphone jack.
good luck