How to keep a nail from falling out of stone fireplace (manmade stone)

If the hole is still there, use some two part epoxy on the nail and stick it back in the hole. If you need a new hole, drill with a masonry bit into the mortar joint the size of the nail and hammer the nail into the hole.

I would call someone who works with brick and ask what to use to fill the hole. (Not just cover it, but fill it.) Then use a screw not a nail.

Tell the brick mason what you are doing and make sure inserting a screw wouldn't make the mortar crumble. Just for grins, try stuffing steel wool into the hole, as tight as you can (use something small enough to keep pushing it into the hole until you can't get anymore in) and then try to insert a screw. I did this on wood one time but not sure about brick. It wouldn't hurt to try and would cost very little for some steel wool.

Use an epoxy masonry filler and a plastic drywall screw holder and screw. Let it dry and cured before inserting the screw. Make sure it is deep enough to ' hold'.

I would take part of a wooden dowel and hammer it in the spot where the nail was. Cut the part of that does not fit and hammer the nail back in. It should stay tight in the hole.