Yeah I'm gonna agree with Elfwine here.
You're only enforcing his point, that the Romans in the Crisis of the 3rd Century faced even tougher odds than the Western Romans in the 5th century, and managed to pull through.
They faced a united Gaul and Hispania, under a Roman Emperor, with Roman troops that their populace would accept indifferently--in the WEST; in the EAST they faced a Roman Empress with Roman troops. In addition there was invasion, civil war, plague, hyperinflation, decreased trade, and deurbanization.
On the other hand, the Fall of the Empire saw Rome facing brutal--but DISUNITED--tribes who managed to push their way through the Alpine Passes--unthinkable from the time of Gaius Marius--and sack Rome.
This is not just a string of bad luck, it's a road of mismanagement and social unrest. Between the 3rd and 5th centuries were the rise of Christianity, increased reliance on tribes and foederati to provide soldiers, and generous amounts of civil war. This isn't just bad luck or coincidence, it's a result of conscious decisions that didn't look more than about twenty years down the line.
Something drastically changed if the Rome that could beat the Etruscans and Samnites into submission through sheer perseverance, beat around the bush for Hannibal for seventeen years, lose 200,000 men to the Germans through sheer stupidity and yet produce a man like Gaius Marius to save them, conquer the known world; is sacked.
This isn't any inspirational shit, it's just rational; it doesn't make sense for a "string of bad luck" to destroy Rome as it once was.
Also, *hair's breadth*, not "hair's breath", just saying.