This is a VERY broad question and I suspect you won't find an easy answer here, since to answer this properly would require detailed knowledge of everything from the fifth century to the thirteenth. Luckily, I've covered aspects of this question before, so check out my answers on 'Why did the Romans fall regardless of their superiority?' and 'What were the main factors in the decline and fall of the Byzantine Empire?', though they definitely don't cover everything.

It is also important to note that Byzantium never experienced long-term decline. There were many periods of revival and even in the dark years of the seventh century we can find examples of the Byzantines doing reasonably well. As for the decline just before 1204, it can only said to have started c.1180 with the reign of the child-emperor Alexios II. Alexios I, John II and Manuel I before him were all capable rulers. Alexios II was a kid, his successor Andronicus was seemingly a brutal tyrant who was then overthrown by a new dynasty lacking legitimacy, so is it that much of a surprise that political weakness became endemic in these two decades? However, I'm not at all confident about my understanding of the late Byzantine period, so unfortunately you'll have to wait and see if a proper expert can provide a more detailed answer for you.