  We consider the collision model of Ziman {\em et al.} and study the
robustness of $N$-qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear
cluster states. Our results show that $N$-qubit entanglement of GHZ states
would be extremely fragile under collisional decoherence, and that of W states
could be more robust than of linear cluster states. We indicate that the
collision model of Ziman {\em et al.} could provide a physical mechanism to
some known results in this area of investigations. More importantly, we show
that it could give a clue as to how $N$-partite distillable entanglement would
be relatively rare in our macroscopic classical world.
