Analyze in detail the collapses of Rome (200-600 CE).
Before I answer this, I do want to offer a caveat. The decline of the Roman empire is a subject that has been the cause of some historiographical controversy — historians themselves do not agree about the correct methods and ways to analyze and explain the decline of the Roman empire. What I offer is a received account although it is not the only account that exists. (There are dozens, if not scores, more!) Some even question if Rome fell; however, since your question assumes that it did, indeed, decline, we'll take that as our starting point.
You also ask about the collapses of Rome until 600 CE. I'm not sure whether the plural is a typo or whether you're referring to multiple collapses. If it's the latter, I address that at the very end.
Also, the standard date for the 'fall' of Rome is 476 CE when the German prince Odovacar deposed the last of the Roman emperors, Romulus Augustulus. From that date onwards the Roman empire effectively ceased to exist except as a collection of many kingdoms and fiefdoms (many of which fought against one another rendering the former Roman empire a battleground of sorts, something which probably only served to usher in the so-called 'Dark Ages' even faster).
The only way to take ca 600 CE as the date of the collapse is to regard Justinian I, the Byzantine emperor who constructer the Hagia Sophia, as the last of the Romans. There is some credence to this. Although he was part of the 'Roman east,' he did attempt to regain some of the 'Roman west'. His generals even successfully battled the Ostrogoths and the Vandals. However, it would be inaccurate to consider his successors to be part of 'Rome'. Especially since the Byzantine empire flourished for almost a thousand years after western Rome fell.
According to the 18th century historian, Edward Gibbon, Rome fell because of persistent invasion from barbarians. Gibbon felt that the adoption of Christianity had somehow 'emasculated' Rome and left it open to more 'virile' conquerers — indeed, the period between 200 CE and 600 CE was marked by incursions from the Ostrogoths, Visigoths, Huns, and Vandals. This was undoubtedly destabilizing for Rome and was one of the contributing factors for its decline. However, it's not at all obvious that Christianity was responsible for this. Gibbon's explanation also ignores other important factors.
One extremely significant event was the battle of Hadrianople in 378 CE. At this battle, the emperor Valens and around 10000 of his soldiers were killed in a single day by the Goths. This allowed the gradual invasion of Rome by external forces and culminated in the deposition of Romulus Augustulus.
All the warfare, combined with natural disasters such as a plague, had also decimated Rome's population and consequently left it weakened.
Around 300 CE and following, there was also a great economic depression because of problems with the slave trade. Rome may have had superior agricultural technology, but in the absence of labor to take care of this technology, it just felt to disuse, which only aided the economic depression.
Oppressive taxation also crippled Rome and undoubtedly let to its decline.
All of these factors can be tied into the growth of a corrupt political system.
So, repeated invasions and the decline in population that went with it, as well as natural disasters, economic depression, and corrupt politics all eventually led to the collapse of Rome.
Now, if you think that there were collapses, perhaps you're referring to various conquests of the city by invading forces — it was the Visigoths in 410 CE and the Vandals in 455 CE.
This is too complex a topic for a short answer to do it full justice. That's why there are several books on the subject! Here are two recent ones:
Ward-Perkins, Bryan (2005) The Fall of Rome and the End of Civilisation. Oxford University Press.
Heather, Peter (2005) The Fall of the Roman Empire. Macmillan.