Hell, if I wanted to be really spicy, I would argue that what we typically understand as "the Roman Empire", in a cultural and political sense, effectively ended with the 3rd century crisis, and what we've had since then have been increasingly different successor states.
I wouldn't go quite that far, but even in the East there's pretty clearly only successor states after the cataclysm of 1204.
If you want to draw a relatively clear line, it seems to me that the loss of Egypt and the concurrent end of the grain dole is as good a marker as any.
yup the rise of islam and the loss of syria/egypt/etc were a hinge point of the byzantines
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