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Pokemon can only lose the contagious factor if they're in your party at midnight, I think. They'll keep Pokerus if they're stored in the PC, however. The PC is kinda like cryo-stasis, everything in there stays the same no matter how much time passes.
I caught Pokerus myself, I somehow knew I had it before I even looked to make sure, I was like "I have Pokerus..." then I looked at the first Pokemon in my party... and what do you know o.o it has Pokerus.