In my (few) readings about the Byzantine Empire i have come across at least two claims about the empire being able to sustain itself, provided that things had developed differently.
One was in 1071, obviously at Matzikert, had there not been a retreat and the capture of the decent emperor Romanos Diogenes. Even if this all happened still, the cancelling of the treaty between Romanos and Alp-Arslan (due to the byzantine machinations against Romanos) mean that the empire had to continue a war against the seljuks, which slowly cost the loss of the main bulk of Anatolia.
The other is at the 13nth century. The battle of Klokonitsa between the Empire of Thessalonike (Despotate of Epirus) and Bulgaria, and the resulting disastrous defeat of the greek army, meant that the Despotate of Epirus could not continue its march to liberate the rest of the european territories of the empire.
It was argued that if there had been two viable successor states, one in Europe and one in Asia Minor (Empire of Nicaea) then they might have had been able to fend off the continuous attacks by other powers more successfully. Of course they would have had to be allied, or at least not in war with each other.
You can comment on these two points of differentiation in the history of the empire, or mention your own proposed other points