Well, the Romans were quite capable of living at peace (insofar as any ancient state was ever really at peace) during the Imperial period.
But not during the Republican one. You'd be hard pressed to find a single year in whole timespan from the First Samnite War (343 BC) to 15 AD without consular or proconsular armies out campaigning. And in the rare happenstances it was the case, the Senate usually showed concern about potential complacency and set out to find some fight to pick (usually a fairly easy task; Rome was hardly ever short of enemies to pick a fight with).
The Roman Republican system was heavily geared toward war as the fundamental glue keeping the whole structure together, mainly because the Italic allies (and later on, the other allies as well) were paying their tributes in military levies, as opposed to taxes in money or specie as it often happened in most other contemporary empires. Moreover, the reward was mainly in land. This nurtured a self-sustaining cycle of expansion without equals in the Mediterranean world.
It took three major civil wars, interspersed with some minor ones, over the space of merely two generations, to change said system a fair bit. Even then, however, external expansion was absolutely key to Augustus' legitimacy and the process didn't really slow down until under Tiberius, in the aftermath of two major military crises combined; still, most emperors after Tiberius himself put some serious effort in conquest whenever given the opportunity for a century more. At that point, the army had long been a professional force and the civil wars had taught deep lessons, reinforced by the the crisis of 69 AD, so that the appetite for expansion was somewhat reduced; and by then, after all, there wasn't much worth conquering left outside the borders anyway; almost all the easy pickings would be taken by about the time of Trajan.