Procrastination
As a psychological phenomenon, procrastination appears to be as old as consciousness itself. Ancient texts document the human tendency to defer, from Egyptian hieroglyphs advising against postponement to Greek philosophers debating the nature of akrasia, the weakness of will that causes humans to act against their better judgement. The tendency has persisted through every technological revolution, adapting its expression while maintaining its essential character.
Yet procrastination exists only in minds capable of conceiving of time and obligation. Should human consciousness disappear, so too would procrastination. It has no independent existence beyond the neural architectures that generate it. Its longevity is entirely contingent upon the continued survival of beings capable of having things to do and choosing not to do them.
Waterfall
Waterfalls have been falling for billions of years, predating not only human consciousness but multicellular life itself. The oldest continuously flowing waterfalls have witnessed the evolution of every species currently inhabiting the planet. They will continue falling long after the species currently worrying about deadlines has completed its evolutionary journey.
The longevity of waterfalls is limited only by geological processes operating on timescales that render human civilisation a momentary flicker. Erosion gradually reshapes them, but this occurs over millions of years. The waterfall that exists today will, in some form, persist long after the last procrastinator has finally completed their final task or died trying.