Well, if a Pokemon uses Skill Swap on Traunt, does the Pokemon continue to sit out turns?
This is my logic going into this. You lose your ability when you mega evolve, so it's no longer in play and it gets replaced with a new ability (though some Megas keep their abilities, like Tyranitar). While I don't have solid proof, I am very certain that once a Pokemon that has a different ability before mega evolving evolves, the effect of its previous ability will go away.
Hope this helps! :)