Deathly Hallows strongly implies that the owners of the Cloak never died until they chose to:

But that night, another wizard stole the wand and slit the brother's throat for good measure. And so Death took the first brother for his own. The second brother journeyed to his home when he took the stone in turn in thrice in hand. To his delight, the girl he once hoped to marry before her untimely death appeared before him. Yet soon she turned sad and cold for she did not belong in the mortal world. Driven mad by hopeless longing, the second brother killed himself so as to join her. And so Death took the second brother. As for the third brother, Death searched for many years but was never able to find him only when he attained a great age that the youngest brother shed the Cloak of Invisibility and give it to his son. And then he greeted Death as an old friend and went with him gladly, departing this life as equals.

(Of course, James didn't choose to die at Voldemort's hand, so it's tempting to read this as "the Cloak defends against old age rather than dying period" - except in canon, James had lent the Cloak to Dumbledore before he was murdered, so for all we know, it really does grant effective immortality/invulnerability!)