It's worth noting that the Roman Republic did survive for a very long time. Despite its longevity, however, instability and turmoil seem to have been built into the Roman political system from very early on, with its political bifurcation between the patrician elites and the far more numerous plebs. The history of Roman politics was one of near continuous struggle between those two groups, with the Plebeians gradually winning greater influence over time.
At the same time, warfare was a critical component of Roman political life as well, dating back to the early history of the Republic. Politically, military exploits were the foundation on which the Roman elite could build their reputation while, economically, warfare provided the Roman population with wealth and land. Long before Roman power expanded throughout the larger Mediterranean World, it had already expanded across Italy itself.
As Roman power expanded, however, the wealth gaps between the powerful and impoverished grew with it, intensifying the economic and political tensions long present within the Roman State. The Gracchi brothers awakened populist strains in Roman politics, mobilizing support among the plebs. Furthermore, the military demands of the expanded Roman State necessitated reforms within the Roman army. Thus, the Marian Reforms played a critical role in this history as well, which expanded the recruitment base of the Roman military but, in practice, had the effect of tying personal loyalty within the army more closely than ever with the commanders rather than with the Roman Republic itself.
These factors served as the context from which the Civil Wars of the Late Republic emerged, perhaps the most famous of which was the conflict through which Julius Caesar emerged as the dominant power in Roman politics—before being assassinated himself. However, this history of intense internal turmoil would continue after Caesar's death and would only be resolved with the rise of Augustus Caesar and the establishment of Imperial Rule.