I've been reading Decker's "The Byzantine Art of War" and have been fascinated by the author's continuous notion that Byzantium was probably the only empire in history that had managed to absorb waves of incursions, attacks and occupations/losses of land but always managing to eventually survive. The empire would then gradually respond and fight back, even capturing long-lost lands.
Vivid examples of such a historical recurrence of survival were the calculated Persian invasions of the early 7th century, the sweeping, surprising Arab conquests of the late 7th century, the Slav occupation of the Balkans during the 8th century, the Seljuk invasions of the 11th century, the treacherous Latin occupation of Constantinople of the early 13th century and finally the Ottoman expansion of the 14th-15th centuries.
Apart from the last wave of attack, the Empire had managed to survive and respond against all of its former assailants for a great part of a millennium. In most cases successfully.
The causes for such a persistence in surviving are numerous, including the highly evolved military structure of the Empire, heir to the known Roman military machine of the past, an intricate level of diplomatic abilities, a rich source of gold, geography and in some cases pure luck.