How it works here: If you are a man aged 18-65 (women had it worse because of maternity leave, but that is not much of an issue anymore) and you are willing to put ut with all the cons the job has, it´s pretty stable job. However, the fluctation of work power is still pretty high because, not everyone is able to live with the cons of the job. Zoos rarely make cuts, people mostly quit by themselves.
Zoo´s here run on very tight budgets so there is no room for being overstaffed. Somewhere it´s actually opposite problem - some zoos don´t have enough zookeepers, e11ither because they can´t find fitting candidate, or because the zoo directory said "xx zookepers is enough" and guess what, it actually isn´t, but why bother playing with budget to make space for some extra wages when we can solve it by volunteers).