The fall of Rome is a subject that gets a lot of attention in history articles, but I think that the deterioration of Rome politically from the early days of the Roman republic to the fall of the republic is more interesting.
In the early days of the republic, in the 400s and 300s BCE, Rome's aristocrats and plebeians compromised. The plebeians had their assemblies, the aristocrats had their senate. The compromise gave common Roman soldiers a sense that in war they were fighting for their own interests. It enhanced their morale and strengthened Rome as a military power.
This broke down when Rome's privileged senators fought reforms that would give benefits to veterans. The aristocrats resisted land reform. Rather than compromise, a politics by violence developed that eventually led to the rise of Octavian, the late Julius Caesar's nephew and the exalted hero of the war against Antony and Cleopatra. Octavian wanted to remake Rome to what it had been in the grand days three centuries earlier. He dislike the monarchical system of government, and he certainly did not want a democracy. What emerged was rule by autocrats with the senate weakened, afraid of the autocrat's power and rubber stamping the autocrats policies. These autocrats were called emperors. Octavian received the title Augustus Caesar. He was Rome's first emperor.
What is popularly known as the fall of the Roman Republic is recognized as having taken place across a couple of centuries rather than overnight. Emperors passed rule to their sons -- a new beginning for European monarchies. In Rome the politics of brute force remained, with assassination a part of it. There was Caracalla trying to end his emperor-father's death sooner rather than later and murdering his brother in front of his mother rather than share power with his brother as the father had wished.
Why Did the Roman Empire Fall?
The question why the Roman Empire fell should be reworded. The question is why did it disintegrate.
It did so because its political make-up left it unable to defend itself against invasion. The Roman Empire was disunited and with many inside it opposed centralized authority: the city of Rome (although Rome had long before been swallowed by its empire). Empires are not nations, and empires are by nature authoritarian. Rome's emperors feared arming their subjects, and many within the empire lacked the sense that "Roman" rule was worth protecting. The empire's military security was not communities of men ready for mobilization at command from central authority. Instead, people from outside the empire were able to march into the empire with only feeble opposition.
Around the year 395, Huns pushed on Germanic peoples, and these Germans crossed the Danube River in great numbers into the Roman province of Pannonia, and the Roman population there fled westward. The empire was further challenged in 399 when Alaric and his army of Visigoth warriors and civilians moved across the Alps and into Italy. Then, in the winter of 406-7, a coalition of Germanic warrior tribes with their farm animals and children crossed the frozen Rhine River into Gaul. The invaders found only feeble opposition as they spread out, some of them going as far as the Pyrenees Mountains, while only a few towns, among them Toulouse, attempted a significant resistance.
Granted, communications were slower for central Roman authority than communications are today, but the question is why Rome fell given the technological circumstances of those times. Some dislike singular explanations and prefer a host of equivalent contributions to the empire's breakup. There are subsidiary factors, namely all that went into the political decay within Rome and its empire. There was the economic decay that accompanied the political decay. Some add Christianity to the mix of causes, and some add paganism. These aside, the political system was geared for occasional failures in competent leadership. And one might want to throw in an increase in population among those living outside the Roman Empire.
Refraining from mixing the subsidiary with the primary, I claim again that "Rome fell" because of its political make-up. This includes division within the Western half of the empire and division between the two halves: Rome and Constantinople. Divisions weaken, and the western half of the empire -- Rome -- was left unable to defend itself militarily against invading armies.