However, the question could also be broadened. What causes the downfall of empires?
An interesting case is the numerous empires that dominated Arabia. The Assyrians fell to the Medes, an internal enemy (I think), who then succumbed to the Persians (also an internal enemy), who were smashed by Alexander the Great. After Alexander there was what could perhaps be described as a bloody enormous Macedonian civil war over his empire, and eventually Seleucus ended up with most of what was Persia. The Seleucid Empire then fell to the Parthians (arguably an internal enemy), who were taken over by a rejuvenated Persia.
Persia ended up falling, permanently, to Islamic armies. However, that means that there were just two clear examples of external armies (Macedonian and Islamic) taking out Arabian empires, compared to a more common pattern of internal enemies (rebels or not quite subjugated peoples) taking over.
Both Roman and Byzantine Empires suffered a tremendously damaging pattern of civil wars in the prolonged preamble to their final destruction. Naturally, both fell to external enemies ultimately (rather bizarrely, Byzantium briefly fell to a Western foe prior to the ultimate end at the hands of the Ottoman Turks) but their strength had been severely sapped (Rome especially) by interminable infighting.
This leads to another question: why was there so much infighting? Rome was acknowledged as the centre of the civilised world, filled with wealth and wonder. The problem was that its leader was the emperor, but Augustus had never actually defined any sort of legal qualification or anything similar regarding who the emperor ought to be. And, as he came to power by the sword, so that system remained. The problem was twofold: firstly, anyone with a bloody big army (and Rome had quite a few of these) might be tempted by the purple. Secondly, and worse, the armies themselves got massive bonuses, effectively, every time there was a new emperor (Danegeld, almost) so they’d often force an unwilling man to assume the imperial title. The poor sod in question could refuse, at which point he’d be murdered, so most did not.
The constant infighting decreased manpower (which was also ravaged by a persistent and virulent plague for much of the 3rd century) and killed off many fine generals and veteran soldiers, creating easy in-roads for the barbarians. Lack of manpower then caused many of the same barbarians to be enlisted in the armies, but they lacked the discipline and patriotism of Roman soldiers, exacerbating the rebellious tendency of the army.
The secret of Rome’s victory over Hannibal was not Scipio Africanus, great though he was, but the burning fire of patriotism and willingness to fight and die for Rome even after Cannae. That fire was suffocated by insensible luxury, undeserved riches inherited from a bygone era of glory and the gates of Rome ended up being thrown open to barbarians who were not fit to lick Hannibal’s boots or be slain by Africanus’ legions.
Still, the joy of history is that we can read and learn, and avoid making the same mistakes today. After all, it’s not like Europe is gripped with perpetual infighting, lack of discipline and economic incompetence, is it?