One possible way to evade the instability mentioned by Tim B would be if some humans, for unknown reasons, repel zombies. That has to be a non-inherited trait (because otherwise soon immune humans would dominate, and you'd end up with humans and Zombies just living separately).
Those who repel zombies would themselves be safe (and being in their vicinity would also make others safe), but they also cannot hunt zombies. But since that trait is not inherited, there will always be both humans who are safe and humans who aren't.
The main problem is, then, to determine the probability for a human to be born anti-zombie. If that probability is too low, there would not be a sustainable population. If that probability is too high, the effect would mostly me as if all of then were protected, because people could simply always keep in groups, where the probability of some anti-zombie then is very high.
The second question is how far the effect reaches. Of course the effect has to be strong enough that the zombie doesn't get in a range where it can be killed (or otherwise the anti-zombies would be very efficient zombie killers). On the other hand, you don't want the range to be too large, because otherwise any settlement could be easily protected by just having a few anti-zombies living at strategic places; if the border of a city is sufficiently stuffed with anti-zombies, the inner part should be protected as well, since the zombies cannot pass the border.
One way to reduce this effect would be if zombies can feel being seen by an anti-zombie and that is when they are repelled, so an anti-zombie cannot hide and hunt zombies, nor can he give absolute protection (for example, while he sleeps, he's not protected, nor are others; also if the zombie is behind him or hidden behind a wall, he will not repel that zombie).
So let's assume that anti-zombies have the ability to repel zombies by just looking at them, but are unprotected against zombies they don't see. That way, the anti-zombies can only give effective protection as long as they are awake and looking in the right direction. Of course when zombified, an anti-zombie loses his special ability (as a special twist, a zombified anti-zombie might be able to resist the repelling effect of being seen by an anti-zombie for a certain time)
It is likely that towns would be guarded by anti-zombie guards watching their borders. So the number of anti-zombies must be low enough that they are not sufficient to prevent all zombie attacks.
Another way to avoid the instability is if a zombie attack is not the only way a human can be zombified; just like with the plague, zombification could be additionally brought by animals (rats, mice, whatever), so zombies might pop up occasionally in apparently safe regions. Then even if humans at some time managed to kill all zombies, suddenly a new zombie outbreak could be caused by a zombie-rat.