Same issue. I have also got the card replaced from the service center, as it has a 10 year warranty. however the same issue started with the new as well. i have lost my data twice now. I am not sure if the Moto X supports any card at all, or Just not the SDXC cards.
Also, I am not a tech enthusiast, so if there's any remedy for it that i can do without actually getting a degree in IT, then kindly suggest.