It is unclear, and up to the DM
Unlike wall of force, which states that the wall can be "free floating or resting on a solid surface", wall of fire says only that it must initially be cast on a solid surface.
The arguments for it staying floating in place are that it's a spell effect, and what's more it's a non-solid spell effect; it wouldn't make sense for it to fall with its surface. For example, wall of ice specifies that the wall is an object that can be breached; no such wording occurs in wall of fire.
The arguments against it floating in place is that it's clearly cast onto a solid surface, which suggests it requires a solid surface. This means it would either fall with the surface, or fail when it falls (although no text suggests this).
I would recommend, if you're the DM, choosing one approach (for this and other, similar, wall spells) and sticking with it, even if that approach is "player's choice". If you're the player, check with your DM.