Hey!
Maybe you should just change the jack.It should have a bad swicth inside.Try to spray some contact cleaner first.Or maybe is the relay..if there is any, clean it.I remember I had the same problem many years ago with a Roland E86.I just change the jack.
But I dont know where you can get one for your X...maybe an external swicht will do the job,a small one doesn't harm the keyboard.
Vio