Depends on *which* plastic. Some are much more stable than others and they all have different storage requirements - polycarbonate is resistant to most things but not to sunlight, for example. Ebonite (the greenish-black stuff used for clarinet mouthpieces) is susceptible to acids, gives off acid fumes as it decays, and so it undergoes accelerating deterioration if one decaying ebonite object is kept in the same case as a bunch of previously intact ones. Polyethylene is resistant to most chemicals and not much affected by light, but can embrittle over decades so it shatters like glass.

The worst is cellulose nitrate, used in prewar hard shiny objects (accordion cases, billiard balls, spectacle frames and the like). Not only does it crumble, it becomes a fire and explosion hazard. A typical old accordion has about as much stored energy as a stick of dynamite. It was used as the base for movie film until the 1930s, which makes movie archiving the sort of business you go into when the thrill of running a nuclear waste repository starts to seem too mundane.