Well, Rome wasn't sacked between 390 BCE and 410 CE, which isn't a terrible run all things considered. The numerous (three) sacks of the fifth century came about because the administrative structure of the empire was imploding around that time, particularly in the Western half. Pressures along the frontier and civil conflict created a feedback loop, and by 410 CE, the emperors had a fairly variable degree of control over their armies and the provinces were heavily infiltrated by Germanic tribes. This process was not helped by the execution in 408 CE of Stilicho, arguably the last truly successful general of the Western Empire, and the confusion this caused allowed Alaric to lead an army of Goths into Italy and sack Rome in 410 CE.

If you are curious about the fall of Rome in the West, I recommend Adrian Goldsworthy's How Rome Fell for an excellent narrative account.

Your question could use some clarification. What period of time do you mean?

B.C. ~390 Brennus and the Gauls sacked Rome. At this time, Rome was not an empire but a small city state with middling local influence, and it was governed by a republic. Certainly they were not the strongest at this time.

A.D. ~410 Alaric and the Visigoths sacked Rome. At this time, Rome was the dominant empire in the Mediterranean and Europe, but their power had waned. This date is commonly used to mark the fall of the Western Roman Empire though the reality is rather more complex.

From about 200 B.C. to about 300 A.D. Rome dominated the European and Mediterranean world. You could reasonably say they were the strongest empire in that area at that time.

Even so, the city was seriously threatened a few times - in particular by Hannibal's army during the Second Punic War. Also, empires in the western Middle East (Parthian), in China (Han) and in India (Gupta) were of similar strength to Rome during the time of Rome's height.