I think the sack of Constantinople by the Latins in their 4th crusade did more to secure Byzantium's decline than any single action by the Arabs. The Turks merely delivered a coup de grace centuries later.
The period surrounding the Muslim conquests is almost as disruptive in the historical record as the Bronze Age collapse. A lot of writing either gets lost or destroyed during that period. Sources dry up after ominous allusions to doom and gloom. The Latin sack was bad for Constantinople, but isn't nearly that bad.
The emperors were also very aware that the loss of nearly all their holdings was the beginning of the end, and that they were essentially caretakers, only able to delay the end. It's very sobering reading what they wrote.