When British naturalist Charles Darwin sketched out his theory of evolution in the 1859 book "On the Origin of Species" - proposing that biological species change over time through the acquisition of traits that favor survival and reproduction - it provoked a revolution in scientific thought.
I thought they defined persistence as literally the length of time an entity exists. There are many ways to persis under their model.
For non biological systems, it's about being in a energetically favorable state for the environment. For example, while many chemicals will form and break down quickly as their environment changes, with form more stable structures that persist through the shifting environments. These structures are selected for as the basis of potentially new reactions and chemicals.
I haven't given chemistry much thought, but the idea holds pretty well for biological systems.
Ultimately, you're right this is totally a thought piece. However, it's great discussion material.