It is possible, and used to be common. When was the last time fucking Visa or MasterCard went down? As far as I know, they don't, because the system operates more like a mesh network. They also use IBM mainframes, which also have a reputation for not going down, at all; those things can contact IBM for replacement parts when their diagnostics report coming failure, and parts can be replaced without turning off the machine. The Multics hardware had the same characteristic, there's a story about turning off part of the machine gradually and reassembling the pieces into a completely separate unit, because it was meant to be used as a utility for computation no different than water or telephone.
This may be a bit of a stretch, but Bitcoin hasn't gone down either. Sure, it doesn't do much in comparison to some of these other examples, but it has never "gone down" globally, now has it?
Something some of these systems have in common is their age. Back when computers were new, they had to work at least as well as what they were replacing, but now they're common and don't work worth a fuck.
Always be careful when deeming something to be impossible. There are a lot of retards in computing who insist that things be impossible, but it's really just an excuse for their pathetic nature and inability.