Ah, one of those questions that is to be answered with 42? () If not: here's my view.
The Romans did have a bit of a problem: money.
You see, when they started the whole thing - I'm talking of the very first Augustus - they had occupied just about every money making part of the Western Hemisphere. In those days modern France, and Spain could pay the little tax that was required to maintain those countries - mostly by slaves. We are talking about an era with 0% inflation for about 100 years, and after that just 0,25% inflation (figures from a BBC show, about how did the Romans, what the EU fails to do?). Italy actually made money in those days.
The trouble began when the whole of Italy didn't make a penny a year - all productivity had moved out of Italy, mostly towards the East. And ever since the Roman state finances system basically boiled down to this: The East (everything East of Italy) pays to keep up the West (Italy and everything West). The West eventually and irrevocably shrank in terms of population, and profit - while the East grew causing famine (as this area was already pushed to the max) and public order trouble.
Seeing this, Emperor Diocletian reorganised the Empire by dividing it into 4 seperate sub-empires. The new administrative centers were: Trier, Mediolanium, Nicomedia, Antioch. After that it was only a matter of time for the Roman Empire to collapse: the single factor that keeped everything together for so long - the fact that everything was turned towards Rome itself - was gone. The 2 Caesars, and the 2 Augustuses weren't driven by a common desire for Roman greatness, whatever Roman thing - they were driven by ambition for their own power, resulting in civil wars and political instability.
Add this to the fact that Rome's income didn't actually grow in all those years: every growth was consumed by larger upkeep costs for their army. Augustus the very first could field about the same amount of usefull (thus active) legions, as the last Emperor ruling the entire Empire.
Add that sum to the new arisen trouble of 'Barbarians' pouring into the Roman world causing social unrest, and new administrative and military difficulties and you have: the Roman Empire was bound not to last.
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