I was infected in round 3, 9 and 11. If I remember correctly, three other players was also infected once each in between round 3 and 9. I was quite easy to take the damage the first two times, but the last time it was one of the border stacks, the Zombies got a lot of troops at the same time, doubled the border stack and was then able to take some two more border stacks as well... Made me quit.
#Zombies, how many times can I get infected?
patent heart
hollow zealot
There is no limit on how many infections you can get per game. The only limiting factor is that every other player has to be infected before you, before you can get infected again. The risk of infection is higher when the zombies are small or completely removed.