In the end, it turned out (as long as we did our best), it didn't really matter. The business was constantly making best guesses at allocation of resources (human, equipment, etc) and hedging that against the customer experience. 100% reliability was never the goal. Violating SLAs and potentially having to give the customer a service credit was just part of the calculus. We were taking it upon ourselves as the most important thing in the world to keep the service up, because that's how it was presented to us, but to the business it was not nearly as important.
If you can de-couple yourself from these stresors somewhat, keep them at arm's length, you'll be doing yourself a great service.