All throwing weapons have durability, but it's not shown on the weapon itself. It's a few (x) durability per quantity, so when x durability gets taken away from the weapon, a quantity point gets taken away, permanently. If you use the titans in melee, it would seem that they would indeed eventually break.
However, if thrown, in v1.10, they will not. Their quantity would return back to normal with the replenish mod. This was not true in v1.09.