Why are simple models of coupled pendulums incapable of describing irreversible energy dissipation?

Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (say, $A$) is displaced keeping the other (i.e. $B$) at rest. As time passes, all the energy of $A$ is transferred to $B$ that was initially at rest. At one point $A$ comes to rest, momentarily and $B$ carries all the energy. Eventually, the situation reverses and the cycle continues back and forth.

In this very simple example, if we regard one of the pendulums (say, $A$) to be our system of interest and $B$ acting as its environment, we see that there is no permanent dissipation of energy of $A$. Even if we track the motion of $A$ only, its energy is not irreversibly lost to $B$ (its environment). It regains all of its energy periodically without any damping.

So this simple example above illustrates that just diving a compound system into two parts and keeping track of the degrees of freedom of one part only will not necessarily lead to dissipation.

The example above could be extended to a system of $n$ coupled oscillators. Here too, starting with a similar initial configuration, if we regard one of the oscillators to be the system, and all the other acting as its environment, the energy of A is not irreversibly lost to the remaining $(n-1)$ oscillators.

Question Why do these models described above fail to capture the phenomenon of dissipation? What are the feature of the environment of an actual pendulum (i.e. a real pendulum immersed in the atmosphere) and its coupling that causes its energy to be irreversibly lost to the environment (the atmosphere)?