I think one of the biggest misconceptions that the average person has about chemical compounds is to think of them as unchanging. The reality is a lot more complicated. Exchange of like atoms (oxygen for oxygen, or hydrogen for hydrogen say) is always going on. We know this from stable isotope studies and even from radioactive tracer work, among many other reasons and evidence.

Systems are not static at the atomic level, at the molecular level. More like a giant square dance, where the overall form is constant but individual partners move around, trade places. The rate of trading (and how far a trade partner can migrate away) varies considerably depending on the physical state of the compound, whether solid, liquid, or gas. Solids are slowest and gases are fastest, as a general idea.

People talk about things like a water molecule, as if it is something that has existed since it first formed, maybe billions of years ago, but that is not exactly true. In bulk, sure, that mass of 10^23 (1 followed by 23 zeroes, perhaps a cup worth of water) has been water that long, perhaps, but each molecule is constantly smacking other ones and in the process, switching atoms (changing partners). Some of those changes involve other compounds too (the O in CO2 can end up as the O in H2O (water), and the reverse, with time).

It is certainly true that the rate of exchange is highly variable, and depends on the system and things like temperature (amount of energy shared around the system). It is also true that the distance over which such exchange occurs can be very tiny from our point of view. A hydrogen atom moving down a chain of carbon atoms in a solid over time is only moving on the order of nanometers (billionth of a meter), but it is moving. Which particular one is moving, or how many are moving at the same time, or what all is happening in detail is very hard to see or measure, but we can prove that it must have happened, and theory says it should anyway (the world at atom level is really busy).

This is pretty much the idea behind chemical equilibrium, that the compound is stable and persists even if the individual atoms move around. It is a dynamic process, but it is a steady state (what goes one way is offset by things going the other way, and not at all a case of once made, never changes, although some conditions can be, effectively, one-directional, going from all this to only that, when one form is way more stable than the original form). Basically, reactions will proceed primarily in one direction until the rate of reaction coming back gets to be about equal (that is what equilibrium means). Then things just dance together, switching partners (individual atoms or perhaps ion groups, particularly the anion complexes, which tend to migrate as a unit) but not switching the bigger forms that we call compounds.

As to the primary question, the persistence of an organic (or any) chemical compound through time depends on its chemical stability, which depends a lot on its circumstances (what else is nearby and competing for energy and electrons, and how easily can atoms change places, and whether the existing arrangement is more stable than alternatives using the very same atoms).

Some compounds are very easily broken and converted into something else. These compounds are the first to disappear. They also tend to be the simplest compounds (with organic molecules, the short chains will break down fairly easily, but they do get somewhat replaced by the breakdown of bigger chains into shorter chains).

When bacteria or bugs or whatever find these compounds in the environment, they tend to eat them all right up, really fast. These compounds will also break up just from non-biological reasons fairly quickly.

Other different bacteria ("bugs") come along later and try to eat the residues. Some compounds do not yield enough energy to make it worthwhile for bacteria or whatever to even attack them and break them up. Costs more to do that than they get out of it. Those molecules just sit there for eons. No energy benefit for breaking them up even if they might not be the most stable form for what they are made from. The energy wall they need to cross to get to the more stable forms is simply too high for it to happen except rarely.

Other compounds are so stable, or so difficult to split apart, that the still exist after millions of years, changing only slightly between burial and our return to surface in crude oil.

Some compounds persist for so long that we use them as markers, as indicators of which plant (or animal) types are the probably source.

What is the lifespan of an organic molecule? It depends very much where that molecule ends up going and how unstable that molecule would become for new conditions. If you do not change conditions, the stuff will not change very fast if at all. Might still change atoms with near neighbors every so often, but the compound WILL persist.

If you take something like butane (a fairly simple organic molecule), it will last as long as you keep it in a container, but as soon as you flick your bic and press the lever to let gas out, POOF, it is destroyed in flame. Some compounds like PCBs and dioxins are so complex, and so noxious to life, that they persist almost forever, as far as we can tell. That is actually what some compounds we make are called, "forever chemicals", because nothing around our near-earth situation will break them up. We can only break them up at extremely high temperatures in the presence of oxygen or some similar electron-grabber, or in some other fairly difficult way.

How long does an organic compound last? from seconds to billions of years, and pretty well any time in between, depending on what you do to them.