The Jem has an enclosed barrel style jack, and can't be tightened. You'll have to replace the jack. Overall it's a poor design with an average lifespan of about 10 years. The traditional fender style jacks are going strong 50 years later, and can be reconditioned countless times. But the barrell style jack just looks so cool its irresistable to guitar designers. Plus you can design cool recessed things like they do on the Jem, JS, and S guitars.
That's one part where Korea's version is arguably better than a switchcraft or a Japanese version. They designed theirs with a nylon cushion that's more durable than just relying on the spring-back of the metal alone. It's available from Mighty Mite, and both Sam Ash
and Guitar Center carry it in their fake brand name parts, because those are all Mighty Mite parts.