In the PHB it says that three death saving throw failures means you die, and damage causes 1 failure, and a critical hit causes 2 failures. But the unconscious condition says that attacks against an unconscious character have advantage and auto-crit if they're within 5 feet. That seems really tough -- it almost guarantees that you'll die if hit twice if one is melee, and on top of that if you're hit once and not stabilized on your next turn you have a 45% chance of getting your third failure from the saving throw.
Am I correctly reading the rules? If an attack hits you while you're unconscious and making death saving throws, does it cause 2 failed death saves?