This happened to me one time as well, even if I changed jobs the job abilities were gone. It is actually a glitch from the original game itself and has nothing to do with 'add-ons'. There is a fix without re-installing, however.

Instead of using the Playonline Viewer File Check, go to Start Menu > PlayOnline> FINAL FANTASY CONFIG > and on the last tab there is a different file check option there "Final Fantasy File Check Settings" and agree. Use that one and your abilities will be back, this resets all of your game files.