I'm by far no expert - but from a guy that likes to rig everything - LIQUID NAIL fixes everything - hell I've actually used it to put some soles on my flip flops that were falling off bAHAHAHA
Take the piece off and take it to lowes to get caulking that matches the color of what was there, bring it home, clean all the old caulking off.
Liquid nail it to the wall, then let it dry overnight.
Come back the next day and caulk the edge for cosmetics.
You can glue it temporarily, but eventually it will pop off again. You have a problem with the wall behind the marble, probably moisture. Pull the tile and check it. You can buy the right type of quickset to glue it back at Home Depot.