Historians argue over the nature of the Roman army's collapse.

Some believe that the Roman empire's military adapted in response to changing conditions when the empire's leaders realized that conquest and expansion were no longer viable options due to limited economic and natural resources.

The Roman army initially focused on securing their borders and building forts and walls around cities, but this proved to be ineffective as invaders were able to fight their way into the cities.

Priority shifted to defense of frontier areas with Germanic troops from outside the empire.

The military then focused on the development of mobile units who fought enemies as they invaded the empire.

While some believed that a military composed of peasants and mercenaries was not as loyal as the traditional Roman army, others have contended that splitting the empire between Rome in the West and Constantinople in the East and adopting Christianity as the state religion profoundly affected all elements of social and military life.

Christianity questioned the divinity of the emperor which means he had less authority.

Constantinople had more resources and was easier to defend.

Some scholars point out that inflation and poorly equipped units stood little chance of stopping invaders so peasants were commanded by professional soldiers rather than military governors so that they could become more agile.

Thus, the Roman Empire became fragmented as its enemies became more powerful.

Lack of resources and inflation contributed to the eventual collapse of the Roman civilization and the development of smaller states.

Why did the Roman Empire collapse?

The fall of Rome is usually considered to have taken place in 476 A.D. when Odoacer, a minor German chief, captured Rome and forced the emperor off his throne.  But Rome began to decline centuries before that.

A time of peace and prosperity, known as the Pax Romana, began in 27 B.C. when Augustus became emperor and it lasted until 180 A.D. with the end of the reign of Marcus Aurelius.  During the Pax Romana, the government of Rome was stable, and the Roman Empire grew in wealth and power.  This came to an end in 180 A.D. when Commodus, the son of Marcus Aurelius, became emperor. The decline and the ultimate fall of the Roman Empire began with the end of the Pax Romana. The decline of the Rome continued when the Empire was permanently divided into the Eastern (Byzantine) Empire and the Western Roman Empire.

There were several reasons for the decline and fall of the Roman Empire.  First, there were political reasons. There were no rules on who was to inherit the throne. This led to periods of civil war that plagued the Empire.  Between 234 A.D. and 284 A.D. Rome had 26 different emperors. The division of the empire also hurt the western empire. The best generals and administrators were found in the east. Next, there were economic reasons.  More and more money was needed by the emperors in order to pay the army and stay in power. This meant higher taxes which made Romans unhappy and less loyal to the Empire. In addition, no new lands were conquered depriving Rome of new revenues.  Eventually, inflation became a big problem.  The finally, there were foreign enemies.  While Romans bickered and fought over politics and money, they left the frontiers open to invasion. It was the invasion and capture of Rome by Odoacer in 476 that is considered the fall of Rome.

 The beginnings of the decline, or “falling”, of the Roman Empire could probably be traced back to the reign of Commodus and the end of the Pax Romana in 180 A.D.

The Eastern Roman empire while Greek speaking and dwindling over time, fell in 1453 A.D. with the capture of Constantinople.

A plague in the 6th century, interrupted the efforts of Justinian to recapture many of the territories of the Western Empire especially in Italy into the Eastern (Byzantine) Empire.

A large bureaucracy, standing army and resulting heavy taxation played a role in the decline and fall of the Roman Empire

Modern scholars emphasize that Rome did not actually "fall."  They argue that Roman civilization continued to exist long after what is usually known as the "fall" of Rome in 476 AD.  They prefer to say that Roman civilization and the Roman Empire gradually declined.  If, however, we use that date as the time that Rome "fell," the following are important reasons for that collapse.

• Overextension of the Empire.  The Roman Empire got to be so big that it was very hard to administer.  It was also very hard to defend and was in fact impossible to defend just using Roman soldiers.  Therefore, Rome had to use mercenaries to help defend its empire.  This overextension really stressed Rome's ability to govern and defend its empire and weakened Rome considerably.
• Presence of "barbarian" tribes within the Empire.  These tribes had moved in under pressure from other "barbarians" like the Huns.  These barbarians lived in the Empire but were not officially there.  Their presence was a danger to the Empire.
• The political power of the army.  The army held a great deal of power since it was the sold defender of the Empire.  Individual generals who commanded loyalty from their parts of the army became extremely powerful.  They also became ambitious.  It was one of these generals, the mercenary leader Odoacer, who finally overthrew the last Roman emperor in 476.

What caused the fall of the Roman Empire?

This is a very complicated question, and entire books and historical debates have centered around it. Furthermore, you should note that the very question itself is subject to some significant historical criticism. For one thing, note that, when we discuss the fall of the Roman Empire, we're usually only referring to the western half of the Empire. This is important given that the eastern half would last for approximately another thousand years. Historically speaking, narratives involving "the fall of Rome" tend to be fairly problematic and subject to debate.

Beyond this, however, I don't think the subject of Rome's decline and fall can be boiled down to a single root cause. Probably the most dramatic feature was the extreme turmoil (both internal and external) that followed the Pax Romana. Beginning in the reign of Marcus Aurelius, Rome found itself facing significant pressure from frequent population movements and incursions from outside the empire's borders, resulting in military conflict. As if this was not enough, there was also tremendous internal political unrest over the imperial succession. The scale of this political turmoil was extraordinary. According to one historical text,

The years from the assassination of Severus Alexander in 235 to the acclamation of Diocletian in 284 witnessed rapid, often violent political change. In less than fifty years, at least eighteen emperors took power with their legitimacy confirmed or ratified by the Roman senate. Even more men claimed to be Princeps without such sanction...most met a violent death (Mary T. Boatwright, Daniel J. Gargola, and Richard J. A. Talbert, The Romans: From Village to Empire, New York: Oxford University Press, 2004, p. 432).

What you can observe in this situation was a polity in crisis. Furthermore, as if this was not enough, it should also be noted that the Empire was facing significant economic distress as well, which would have further weakened it. Even so, note that the Western Empire continued to endure through this long decline.