I can't say that I really buy that. Wealth was always concentrated in Rome. I'm going to assume that you mean the Western Roman Empire because the whole Roman Empire lasted until 1453 although there was a brief time that Crusaders took it over. If it were true, both sides of the empire would have fallen since they both operated the same.

The Empire definitely had quite a few issues. The debasement of the coinage led to some pretty significant inflation. It got so bad that Diocletian basically got rid of the mint and went with a very complex goods conversion system. But that was in the 3rd century. The Western Roman Empire had a hell of a lot more tribes bordering them to contend with while the East largely just had the Sassanids. The rules of succession were pretty lax too and many emperors avoided making successors until their death bed. That is fine if the emperor has a slow and predictable death but when they didn't, people (often military leaders) would simply claim they were emperor and take their armies and take over. That gave an opening for outside tribes to take advantage of the chaos.