Here's what happens for those playing the home game:
I withdraw my Galagladi (Gallade) from the PC and put him in front, with Prof right beside him. I go out and battle with Galagladi. After each battle, I check Prof's status to see if he's infected.
Once he's infected, I go back to the PokeCenter and heal the party. Galagladi goes back in the PC.
I double-check Prof's status and save.
The next day, when I play, I checked Prof's status and the Pokerus status is gone, but the recovery symbol isn't there. And since I've been able to infect him three times, then obviously the infection status isn't being held.
This time, I used my Zapdos carrier. My Zapdos has a strain from my Tropius, which is the strain I usually use. I again infect Prof, saved multiple times, and decided to test a theory by restarting the game.
The infection is still there. However, there are additional factors at play; one being the internal clock. I'll only be sure if the infection took by checking tomorrow.
Another option is to box Prof for the night.