In recent years, self-healing materials have attracted increasing attention due to their potentially spontaneous self-repairing ability after mechanical damage. Here, we focus on a supramolecular self-healing rubber based on fatty acids following the work of Leibler and co-workers. We study the heterogeneous network structure and hydrogen bond dynamics as well as its significant aging properties using several experimental techniques. NMR experiments reveal that the rubber is basically a two-component system, with a similar to 85% fraction of material rich in hydrogen-bonded structures and associated aliphatic moieties, undergoing a glass transition just below ambient temperature, and the other one being comprised of more mobile aliphatic chains. Changes in the IR bands corresponding to the NH bending and CO stretching vibrations show that water in the rubber not only takes the role of a plasticizer, reducing the glass transition temperature of the main component, but also is involved in changes of the hydrogen-bonding network. On the basis of shear rheology experiments and proton low-field NMR, we deduce that the rubber undergoes irreversible chemical cross-linking reactions at temperatures above 110 degrees C, going along with a weakening of its self-healing ability.