To clarify on everything..
- Pokérus may expire at midnight(12:00am) if the infectee is in your party at this time.
- There is a chance that Pokérus will spread to adjacent party Pokémon after each battle.
- To preserve contagious Pokérus(represented by the purple "Pkrs" icon by the summary sprite), just make sure it is in a PC box before 12:00am.
- The smiley face symbol that appears upon expiring, means that the infection is no longer spreadable, but the Pokémon will still gain the x2 effect on EV gain.
That should cover more or less everything that gets asked so often :P