Hey there!
The Roman republic was one of the greatest republics/empires the world ahd ever known. They controlled the entire Mediterranean Region which allowed Romans to call it the Mare Nostrum, or "our sea" in Latin, had may advancements in engineering and language, and left an unforgettable legacy behind.
When Rome fell, the days of the republic were long over. It was after clever Augustus Caesar, or Octavian had tricked the Roman senate into believing he was restoring the power of the republic and created an empire. However, after many years, as history never fails to repeat itself when the past isn't learned from- the empire fell and was broken into many "sub- empires", one of whuch was the famous Byzantine. Many factors led to this sudden demise.
One was the size of the empire. The outrageous size of the empire made it very hard to defend, and instead of working to expand the reach of Roman authority, the empire was too busy defending it.
Also, the army consisted of a lot of mercenary soldiers, who were not loyal to Rome. The size of the army required pay for all soldiers, so the empire charged heavy taxes upon its people, and therefore many became impoverished. This made many people poor, hungry, and dying.
Additionally, the emperors were not very loyal to the empire. Following the rule of emperor Commodus, (whom was very selfish) emperors began to become very, very corrupt. They often took advantage of the treasury to pay debts and take money for themselves. This made money worth less and less.
This unusual spending led to inflation. Prices of goods went up, and money was worth less. This was because the amount of money a coin was worth depended on the amount of silver in the coin. The empire was short on silver, and as a result they could not put as much and money was worth less. Over time, Roman money became worthless.
Emperors could not transfer power peacefully. Often, emperors were murdered by the Praetorian Guard (comparable to the "secret service"), and after rulers died, great civil wars often broke out and killed many people.
While all this was going on, as Romans were dying, emperors were becoming more corrupt, and money became worthless, Germanic tribes began pushing on the borders and were so powerful, the emperor could simply not defeat them. Soon, Rome simply fell.
There were many disadvantages of an empire compared to a republic. First of all, there were no checks and balances. The emperor was considered a god (when Christianity came, that belief changed), and had unchecked power. However, in a republic, power was shared among consuls, the senate, and more. This allowed the empire to make decisions that were more thought through and in favor of the people. Perhaps maintaining the republic would have kept Rome alive. Remember that emperors were not always strong and honest. Often they were weak, and corrupt. That didn't occur with the republic. If a consul, senator, or someone else in power was corrupt or dishonest, another person in government could veto their actions, just like we do in America today. In fact, our government system today is based off of that of the Romans- for example, our Bill of rights is modeled after the Romanesque 12 tables or tablets in the times of the Republic, which was one of the first examples of written law.
If you're interested in finding out more about this topic, I suggest reading "The Decline and Fall of the Roman Empire" by Edward Gibbon.
Hope this helps!