Self-perpetuation

Self-perpetuation, the capability of something to cause itself to continue to exist, is one of the main characteristics of life. Organisms' capability of reproduction leads to self-perpetuation of the species, if not to the individual. Populations self-perpetuate and grow. Entire ecosystems show homeostasis, and thus perpetuate themselves.[1][2] The slow modifying effect of succession and similar shifts in the composition of the system can, however, not be neglected in the long run.[3] Overall, life's object's capabilities of self-perpetuation are always accompanied by evolution, a perfect steady state of the biological system is never reached. Sexual reproduction is also a form of imperfect self-replication and thus imperfect self-perpetuation because of recombination and mutation. Organisms are not like self-replicating machine but amass random modifications from generation to generation. The property of self-perpetuation in the strict sense thus only applies to life itself.

Look up self-perpetuation in Wiktionary, the free dictionary.

In a social context, self-perpetuation is tied to reflexivity and (usually) positive feedback loops:

To overcome strong prior beliefs, strong evidence to the contrary is needed. If a person is predisposed to choosing a certain action, the advice from an advisor who sets a low threshold for recommending the alternative action is not of much use. The preference for like-minded advisors who supply coarse information implies that the advice a person receives is likely to reinforce his existing priors. This effect can lead to polarisation of opinion and the emergence of self-serving beliefs. The learning process is prolonged and the induced short run bias can become perpetual if information is costly

— Wing Suen[4]

Depending on the time scope or the context, self-perpetuation either depends on self-sustainability, or is equivalent to it. While we may talk about the self-sustainability of an ecosystem, this depends amongst other factor on the self-perpetuation of its constituting species.

In computer science, self-reproducing programs constitute an incomplete metaphor for self-perpetuation. A better analogue can be seen in computer viruses which are actually able to self-reproduce - given a suitable computing environment.