The Five Stages has also been a favorite of mine. I found a copy at a used book store before I had even heard of Gilbert Murray. I still own this mass market paperback copy and read it regularly.
We can distinguish between terminal stages of a civilization with and without a failure of nerve. Murray saw a failure of nerve in late antiquity. Other interpretations are possible. It is salutary to compare Murray's interpretation of late antiquity with Huizinga's interpretation of the "Autumn of the Middle Ages." Huizinga did not suggest any kind of failure of nerve, but nevertheless a civilization in retreat and surrendering to a new order that would replace it. In the case of the yielding of the medieval world to the modern world, we see the antithesis of a failure of nerve: voyages of exploration that mapped the planet entire, and an expanding age of scientific investigation. We do not find anything like this with the collapse of the ancient world, yielding place to the medieval world.
John Romer's interpretation of Byzantine civilization nicely dovetails with Murray's failure of nerve thesis. In the wake of the end of classical antiquity, the continuity of Byzantium expresses itself in a way both distinct from the classical world but also as the exemplification of the retreat from the public work in favor of private spiritual consolation.
Civilizations can come to an end in more than one way.