There are plenty of examples of major nations essentially falling apart or capitulating around this time period (and well after) after losing a handful of major battles (the Persian empire against Alexander and the Macedonians against Rome come to mind along with Pontus under Mithridates).
All of the nations named above capitulated/fell apart after a small number of major defeats (even if they were mixed with some victories) while Rome endured several major defeats at the hands of Hannibal in Italy and Hasdrubal in Spain with no major victories to speak of. How did they do this and why were they able to continue resisting when so many other governments would've sued for peace/suffered a coup/disentigrated?
The works of Roman writers such as Livy, Frontinus, and Juvenal show a grudging admiration for Hannibal. The Romans even built statues of the Carthaginian in the very streets of Rome to advertise their defeat of such a worthy adversary. It is plausible to suggest that Hannibal engendered the greatest fear Rome had towards an enemy. Nevertheless, they grimly refused to admit the possibility of defeat and rejected all overtures for peace; they even refused to accept the ransom of prisoners after Cannae.
During the war there are no reports of revolutions among the Roman citizens, no factions with the Senate desiring peace, no pro-Carthaginian Roman turncoats, no coups. Indeed, throughout the war Roman aristocrats ferociously competed with each other for positions of command to fight against Rome's most dangerous enemy. Hannibal's military genius was not enough to really disturb the Roman political process and the collective political and military capacity of the Roman people.
"It says volumes, too, for their political maturity and respect for constitutional forms that the complicated machinery of government continued to function even amidst disaster—there are few states in the ancient world in which a general who had lost a battle like Cannae would have dared to remain, let alone would have continued to be treated respectfully as head of state" (J. F. Lazenby, The Hannibalic War, 254).
This is something that the Carthaginians found very strange, as it was widespread practice during this time to capitulate once it seemed obvious that your military was weaker. “Hannibal repeatedly stressed that he was not fighting to destroy Rome, but for ‘honour and power’, desiring to remove the limitations imposed on Carthage after the First War and reassert her dominance.”(1) However, the Romans refused to surrender due to their moral principles. The Romans in the senate refused to offer ransom for the prisoners Hannibal held, believing they hadn’t been brave enough. (2) Rome also had a general principle of refusing to surrender, stretching back to the first Punic war where Regulus told Rome to reject a peace treaty with Carthage, even if it meant his death. The Romans then began to rebuild their armies, using younger soldiers (<17), poorer soldiers, slaves, and criminals. To find weapons, the Romans used trophy weapons from temples, that had been taken in previous wars. The trick the Romans then used to control the war in Italy was the creation of multiple smaller armies, instead of one massive one. Hannibal’s army contained his main army of veterans, and then several smaller allies who refused to coordinate, as they all hated the other Italian allies. This meant that the Romans could stall the war out, each army controlling enough space that the smaller armies wouldn’t move, and Hannibal wouldn’t attack Rome. Eventually, Hannibal began to run low on forces and was unable to force victories.
The real question is where the Romans got the idea to completely rewrite warfare during this time and decide what full surrender meant. For some reason, the Romans understood surrender as “dedere se in fidem,” which truly meant unconditional surrender- everything in the state belonged to the Romans. It can be debated if the Romans thought this was the only type of surrender, and that surrendering to Carthage would be akin to giving the entire city to Carthage, but the Romans certainly took their word more seriously than any other Mediterranean civilization.
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