I am no expert but it could be the solder point/s of the jack may have gone bad. A voltage meter would help you determine that. It could also mean the jack itself needs replacing (like you said).
I would open the up the unit and study how it's integrated into the CM board. Use a soldering iron to remove and replace the jack. It's likely the new part wont exactly fit the old one, but this is something you can work around. You would be doing a mod of sorts