What is the lifespan of the original Xbox?
While Microsoft doesn't explicitly say it's okay to do so, there's good evidence that it is in fact perfectly safe to run your Xbox fully powered overnight, and even longer. There are zero warnings or suggestions on any of Microsoft's official Xbox support pages to periodically turn off the console.
How can I make my Xbox last longer?
Highly doubtful that will happen anytime soon. Many game developers and publishers still support the Xbox One range of consoles.