Arnold Toynbee, Herbert Spencer and others noted cycles in civilization. I like Toynbee's challenge-response paradigm myself. If history can be said to repeat itself though one must ask what it is that repeats?
Human beings have innate behavior involving natural functions that are replicated in all individuals. So one wonders if societies and civilizations also have innate behaviors and obviously they do. I value G.W.F. Hegel's quite highly myself though his dialectical paradigm for history being God evolving through history is somewhat over-generalized for use in the particular paradigm of 'does history repeat itself?'
One wants to place human existence on Earth within the broad parameters of Universal existence in a space-time field in order to ask literally if history repeats itself to which we tend to provide a definite 'no'. The space-time continuum is a linear flow with entropy having a direction. In an infinite multiverse however it might be possible that history recurs nearly the same in an infinite number of permutations although each in a different Universe. Again that fairly difficult to pin down paradigm of recurrent historical cycles could be itself just another contingent ontology within God. If God can foreknow and pre-exist in effect all things would he really need to actualize them?
Leaving off the difficult question of the nature of reality-for-humans as a contingent space-time field phenomena for now and returning to the question of 'does history repeat itself' in a narrower interpretation it is possible to break down the question into pieces; do some things in history repeat such as the growth of trees or species if not exterminated, or do weather patterns recur, and do corrupt rulers ever recur in history, do nations end because of excess public debt and so forth. I believe there is evidence to support the idea that civilizations and nations repeat errors just as some people repeat criminal behavior.
The troubles with getting rulers to work for Utopian goals optimizing so far as possible an optimal course of human development tend to recur too for analysts trying to goad a society toward better goals. I think there was a movie maybe starring William Holden 'The Bridge of Toko Ri' or some such that had a recurring effort to destroy the bridge of the bad guys so the good guys could liberate the oppressed, well on second thought I am thinking of another movie about test pilots.
All these test pilots were killed and the project was to find out why-they all kept making the same mistakes or the plane's fault was killing them in the same way; no one knew what it was. Historical mistakes were recurring. I guess if one had many planetary civilizations to consider one might discover that many or most ended their existence by destroying their ecosphere or themselves through war before learning about it. One must hope to avoid repeating the mistakes of the past especially if that involves the hubris of lacking faith in the living, transcendent God.