What were the reasons why Rome's prosperity came to an end and for its eventual demise?
If I understand your question correctly, you are asking why Rome fell. This is one of the classic questions in world history. Many scholars have tried to answer it and there is no clear consensus as to the most important causes. Since different scholars have different answers to this, you should probably check your own text and/or your class notes to see what causes you are supposed to give in your answer.
Although scholars do not all agree about the causes of the fall of Rome, there are some general causes that most people agree on. Let us look at three of them.
First, scholars tend to say that Rome fell partly because of political instability. Rome did not really have a good system for transferring power from one emperor to the next. When one emperor died, there was often conflict between rivals who wanted to be the next emperor. This sort of conflict weakened the empire. Instead of all pulling together, armies and people would take sides in conflicts over power. This weakened Rome.
Second, scholars argue that economic and social problems weakened Rome as well. Because Rome had such a big empire, it needed a huge army. This cost a tremendous amount of money, money which had to be collected in taxes. The taxes hurt the economy and they angered the people. Because the economy was getting weaker, it was harder to maintain the army. Because the people were angry, they were less likely to support the government. This made Rome weaker and more likely to fall.
Finally, Rome fell in part because of the influx of barbarian tribes. During the last couple centuries of the Roman Empire, various barbarian tribes started moving towards the Roman Empire. Many of them moved into the empire and many became part of the army. These barbarians typically had little loyalty to Rome and were not very dedicated to fighting to protect it. Also, the barbarians sometimes actually attacked the Empire. This weakened the Empire as well. It weakened the Empire by killing soldiers and destroying towns, but it also weakened the Empire because it made people lose faith in the Empire’s strength.
These were some of the most important factors that helped to cause the Roman Empire (or at least the Western Empire) to fall.