Found commonalities between the Venus Flytrap, Hippo Enclosure, Sweet Sunflower, and Venomous Flytrap that prevented them from being storable. This has been fixed.

Reminder that if your Exotic Pet is not storable, try collecting from them first. They cannot be stored in their "working" (timer active) state or their "ready" (timer expired) state. Only the "idle" (feedable) state is storable.