Daniel Gilbert actually coined a term called immune neglect (Gilbert et al., 1998), which describes a common bias in affective forecasting. The idea is that when we try to predict how we'll feel following a negative situation, we fail to take into account (i.e., we neglect) that our psychological "immune system" will kick in and return us to some neutral baseline. So we overestimate how bad we'll feel.
Indeed, the idea that we have some homeostatic mechanism(s) (or really, allostatic; Sterling, 2014) that brings us back to some baseline has been thrown around in psychology for a while (e.g., Forgas & Ciarrochi, 2002), but emerging theory is starting to take this idea seriously (e.g., Barrett & Simmons, 2015; Craig, 2003; Sterling, 2014; Sterling & Laughlin, 2015).
So to your main question: what kinds of states make us susceptible to other negative mental states? One answer is a negative prior (e.g., Beck, 1979; Huys, Daw, & Dayan, 2015), which shapes your predictions about the world. For example, if you grew up in a threatening environment, you might develop a prior that yields predictions that the world will be threatening. Indeed, you might even discount evidence against your predictions (i.e., that the world is not threatening).
This is actually considered adaptive--you're using your prior knowledge ("the world is/was threatening") to make predictions about the world ("the world will be threatening") and to guide how much you weight the errors in your predictions ("the world is not threatening"). After all, if you've only been exposed to threat, then it's good to be hypervigilant to more potential threat and hypovigilant to potential indications otherwise.
So--that's what happens in depression, for example. You get "stuck" in a negative state because your negative prior leads you to weight negative information more heavily (Garrett et al., 2014) and ignore "the full range of signals from many sources" (Sterling, 2014). If you fail to change your prior in accordance with new evidence, then you'll behave maladaptively and remain depressed.
I think my answer is slightly incoherent and not complete, and I think there's probably a whole lot more to explain…but I hope it gives you some idea of what's going on.