For that particular mission, it's not the small debuff you get that completes the mission. It's a different infection. You just have to keep fighting rakghouls until you get the mission complete. Any rakghoul will work.
Sometimes you'll get infected very quickly (like in the first 10 seconds) other times it takes forever (1 hour for me last time).
If you see that you are running short on time and are still not infected, open up your mission log and hit the Reset button. This will reset the timer to 1 hour 30 min so you can keep trying.
This has to be the most random mission I've come across. The "strong or elite" theory might help but not always.
Some of our guild have spent (literally) hours trying to get infected, hacking away at every rakghoul they come across. I think 3.5 hours was our guild's record when they finally got credit two zones over.
Our first time through we noticed that the timer reset itself after the initial 45minutes ran out. Might have changed since then.