The empire existed for more then four centuries after the Republic was overthrown.
Yes, but after the republic was overthrown, Rome was on a downward slope and gradually lost its wealth and territory. My point is, all "empires" are doomed to fail, because the model of a nation constantly needing to conquer territory and needing an enormous amount of resources to sustain its infrastructure and military, combined with the fact that once the republic was abolished, citizens and soldiers were loyal to their generals and local rulers than instead of nation itself (which caused corruption and the government to be less efficient than when it was a republic) caused the WRE to collapse.
It seems like all states with a model like that are doomed to fail. To be able to conquer lands and defeat rival nations, you need good generals. Once the people start favoring the generals more than the state, the generals are able to usurp power and that leads to instances such as this.
After the Republic was overthrown, the Romans saw their greatest achievements. After the ascension of Nerva and the Five Good Emperors, Romans saw civic, military, and political success on an unimaginable scale. Trajan, Hadrian, Pious, and Marcus Aurelius. These are some of the most recognizable names in history. It wasn't until the fatal decision to name a family member (Commodus) to the purple that the Romans began the dark and bloody 3rd century crisis. Out of this crisis, the roots of feudalism were born and the loyalty to local generals and administrators was not really born out of some corrupted, unpatriotic Roman spirit, it was born of necessity. The state had simply gotten too big and the emperor(s) could not handle the many invasions and crisises that popped up. The local citizenry depend on these scant few capable individuals because they were there, the state was not.
Also, the late Roman Empire's administration was no more corrupt than of that of the Republic. One of the main contributors to its downfall was the fact the rich:
1) horded their wealth from state tax collectors, leaving the imperial treasury almost completely empty
2) horded the workers on their estates from army recruiters, leaving the imperial armies with no choice but to hire barbarian mercenaries en masse.
In the end, this fall can be greatly attributed to the single-mindedness of the wealthy in both "Republican" (*cough cough* Oligarchical) and Imperial systems. Up until the very last years of the empire (during the Shadow Emperors), their were always capable and just administrators and generals around but they simply were bound within the tight confines the stubborn aristocracy had given them.