First of all.... Once your Pokemon's PKRS is gone, it is over. It cannot have it again. PKRS is a beneficial virus that doubles the number of EVs you will gain by battling a certain Pokemon. It cannot be healed by the Pokemon Center and can be given to another Pokemon of your team. It wears off after a certain time but will stay on your Pokemon if you put it in the Box, though the other Pokemon in the Box will not be infected. The chances of getting is really based upon luck, but not as much as the luck of getting a Shiny Pokemon. The Nurse in the PokeCentre will tell you after healing your Pokemon that it has PKRS.
My source: Serebii
See that little Purple thing beside ''STATUS''? That is the sign which means your Pokemon has PKRS.