Now my suicune has it. I care a lot for that Pokémon! (even though it is beneficial, I want it gone!)
The duration that PokéRus lasts is dependant upon a random number, known to some as the strain of the virus and can last up to 4 days. This gives ample time to spread the virus to other Pokémon. When the PokéRus has gone through the specific amount of time that the strain allows it, the Pokémon will no longer be able to spread PokéRus and it will now have a face on the status screen. However, despite it not being contagious, as of Diamond, Pearl & Platinum, it will still receive the boost of Effort Values so it will forever be good. If you want to keep it being contagious, however, you can keep it in your box and remove it whenever you wish to spread it.
Does it have a face on it? Have you had it in your PC box for a while? Source
If a Pokemon has been infected with Pokerus it will be contagious for 1-3 days approximately. After that time period the effects if Pokerus will remain but it won't pass on to other Pokemon