Yahtzee, I don't think that the constant revival has to be explained that much by the story. If anything, Prince of Persia: The Sands of Time did that pretty well with its constant "Wait, no, that's not how it happened..." thing.
But there are other ways to do that even more subtly. An example that none of the games followed, to my memory, would be a banal tape rewinding. An average gamer, remember those stone age VHS players your parents or if you're a bit older you yourself still keep around in a dusty attic, in a corner? If you do, figure the rest for yourself, it's not that hard, else go educate yourself, you ignorant twat!
If you rather go into SF territory, a version about a multiverse would be appropriate, and you don't even need to make it man-made. Just assume you, as a protagonist are being plagued by an uncertain quantum state (purely scientifically speaking a complete rubbish on macro scale, unless you've been turned into a Bose-Einstein condensate, but you wouldn't survive that much punishment in all probability) and the only way to achieve certainty is to complete certain tasks, such as assassinating the main villain or perhaps snuggling your cat named Snuggles. The point is that you will remain in that state of quantum uncertainty, thus being unable to die, until as I said earlier you can finish that one particular task.
I could probably think of a dozen more methods, and I probably will use such one in my own game.
Coming back at you, Yahtzee. How can a game punish us except by taking away our precious time? Even on hardcore in Diablo 2, where you would lose your character once you died, in the end you would still just lose time. Who stops you from just making another and starting all over again? That's a massive time loss, compared to modern games, but in the essence it still is nothing more than a time loss. If an optical medium with your game would explode after your unfortunate in-game death, that would be another story.
My point is there are ways to be creative here, not only in terms of a story, but in terms of gameplay that always comes first in a good game. Death doesn't have to be punishing in a traditional sense. Since all the punishment it can give us is temporal in nature anyway.
Still probably the best game in that field, as much in story as in gameplay department was "Omikron: The Nomad Soul". You as a character were a gamer (read: you yourself), or more particularly a player's soul (read: your soul, if such a thing even exists) that was sucked into a dying world by a demonic force. If you died you would just enter a body of a person that happened to be closest to you at a time. That game was a great effort at innovating things like that. An underrated gem, highly recommended.