What factors, internal and external, might explain the success of th Byzantine Empire's survival for so many centuries/ What were the factors which led o its ultimate decline and fall
Cause of Success
Cause of Decline
Google Books is a good place to look for information about questions such as the ones you've raised. Google Books offers extensive previews of many books. (So does Amazon; you can use their preview feature if you have an Amazon account, which costs nothing.) The best books to look for are ones that have been peer reviewed -- in other words, assessed and approved by other experts. Usually these books are published by university presses. Anyone can publish a book these days (just as anyone can slap up a web site or post to wikipedia), so it's even more important now than it was in the past to look for information that has been peer reviewed. Here is a good place to begin a search of the topic you've raised:
Here are some useful links:
The first link explains the rise and fall of the Byzantine Empire, and the second link focuses on its decline. In short, the decline lasted over many years and was mostly due to the empire’s overextension.